Lancaster, 42, will lead England into their home Rugby World Cup in 2015 after seeing off competition for the job from Nick Mallett.
Lancaster's permanent appointment follows his successful reign as interim head coach, during which he led England to second place in the RBS 6 Nations and rebuilt the reputation of the national team.
Lancaster's appointment was proposed by the RFU's new chief executive Ian Ritchie, who oversaw the recruitment process, and was ratified unanimously by the board.
"I am immensely honoured and proud to accept this role," said Lancaster.
"From the hundreds of messages I received during the Six Nations I know what supporting England means to millions of people and I am privileged to be involved.
"The players, coaches and the management were superb during the tournament and it's down to them that we made such positive steps from when we first met up in Leeds.
"The challenge now is to take this squad and the players we will see emerge forward to 2015. It is one that I can't wait to get stuck into.
"We have a massive task ahead of us in South Africa this summer and we have 37 games before that first World Cup match on home soil, so every second counts in developing players who can win that tournament - which has to be the ultimate aim.
"I want to thank Ian and the panel for giving me the chance to explain my vision for England Rugby and, with their backing, I feel very positive about the future."
It has been a remarkable rise from relative obscurity for Lancaster, a former school teacher who spent two years as director of rugby at Leeds before joining the RFU.
Lancaster stepped up from his dual role as Saxons coach and the RFU's head of elite player development to lead England into the Six Nations after Martin Johnson stood down in December.
England had just crashed out of the World Cup in the quarter-finals and the subsequent leaked reports indicated a squad riven by distrust and competing agendas.
At that stage, the RFU had already contacted Mallett and Lancaster was not deemed to be a realistic long-term candidate given his inexperience at Test level.
But Lancaster rebuilt the England team on the pitch and they rounded off the Six Nations with a victory over World Cup finalists France in Paris and a 30-9 thumping of Ireland at Twickenham.
Off the pitch, Lancaster's efforts in restoring the reputation of English rugby won him immediate admirers within Twickenham's executive team.
Lancaster engaged with sponsors and media and succeeded in his stated aim of reconnecting the England team with the public, holding an open training session in Leeds and running community coaching projects.
Lancaster also clamped down hard on ill-discipline, setting the tone by omitting Danny Care from his Six Nations squad after he was arrested - and subsequently convicted - for drink driving.
There was a wave of public support behind Lancaster even though he did not have the sustained top level coaching experience of candidates such as Mallett and Jake White, who ultimately pulled out of the process.
But Lancaster, who was interviewed last Thursday, demonstrated to Ritchie and his four-man advisory panel that he has both the vision and the qualities required to deliver England success at the 2015 World Cup.
Ritchie consulted with Conor O'Shea, Ian McGeechan, Rob Andrew and Richard Hill before presenting Lancaster's name to the RFU board.
"We have been through a rigorous and global selection process and are confident that Stuart is the right person to lead England forward into the 2015 Rugby World Cup," Ritchie said.
"He has shown throughout the RBS 6 Nations and subsequently in both interview and other conversations I, as chairman of the advisory panel, have had with him that he has the skills and vision needed to be the England head coach.
"I would also like to thank the advisory panel for their time and invaluable advice during the course of the process. I have been very lucky to be able to draw upon great rugby expertise and for that I am grateful.
"I am sure everyone in England will join me in congratulating Stuart on his appointment. He can be assured of my support and everyone in the union as he embarks on what we all hope will be a successful period for English rugby."
Danny Cipriani, who will return to England contention next season when he joins Sale Sharks from the Melbourne Rebels, said on Twitter: "Congratulations to Stuart Lancaster. His passion is 2nd to none".
Rugby Players Association chief executive Damian Hopley said: ""I am absolutely thrilled for Stuart and we have all been thoroughly impressed by his professional approach, vision and dedication to achieving the best for English rugby from the day he was appointed interim head coach.
"Stuart is tremendously popular with the players and quickly earned their respect and trust through his honesty, humility and strong work ethic.
"It is to his and his coaching team's immense credit that they helped to transform the outlook and fortunes of the England squad and have instilled such a strong confidence and culture within the squad in such a short space of time.
"I believe this appointment to be an excellent decision for the players and the future of English rugby and I look forward to working closely with Stuart and the players going forward."
But not everyone agrees. England World Cup winner Ben Cohen believes the RFU have made a mistake.
"I don't think he is the right man," Cohen told talkSPORT radio.
"I think he is a man to keep around the squad for the future most definitely and have someone with a bit of experience around that who has maybe got experience in World Cups.
"Nick Mallett has got credentials coming out of his ears, he has got a great CV. And Wayne Smith. They are people who know how to react in tough times."
England play South Africa four times this year plus Australia, New Zealand and Fiji. If they are not ranked in the world's top four by December England will miss out on top seeding for the World Cup.
"Let's be frank, you look at the Six Nations as a honeymoon period and there are testing times to come ahead," Cohen said.
"Yes, he will learn from every game and every situation he has and he has got four years to build up to the World Cup but you want someone who has got experience of managing through that. That's how I see it. Hopefully I am wrong and I will have egg on my face in 18 months' time.
"Will he have the experience and will he have the coaching team he had in the Six Nations? I think it is going to be a watch-this-space scenario."
Lancaster is thought to have argued in his interview that he wanted to retain his interim coaching team of Graham Rowntree and Andy Farrell.
Farrell was seconded to England for the Six Nations but he remains under contract at Saracens, who say the RFU have not been in contact.
New Zealand's attack specialist Wayne Smith has also been linked with a role in the England set-up and is on the record as saying he is keen on a return to international rugby after helping the All Blacks win the 2011 World Cup.
England's World Cup-winning coach Sir Clive Woodward sent a message of congratulations to Lancaster on his appointment.
Woodward, director of sport at the British Olympic Association, said: "I would like to extend my congratulations to Stuart Lancaster on his appointment as England rugby head coach.
"The performance of the England team during the recent Six Nations Championship demonstrated great progress and I wish Stuart and his team continued success.
"The London 2012 Olympics is the start of an exciting series of major sporting events taking place in the UK during the coming years, representing a golden opportunity for British sport.
"Here at the British Olympic Association we are very aware of the significance of enthusiastic home support and I am sure Stuart and his team will enjoy England rugby supporters' full backing going forward towards the Rugby World Cup in 2015 on home soil.
"With regards to rugby joining the Olympic family, I am looking forward to working with the RFU and all of the other Home Unions to ensure the introduction of rugby sevens to the Olympic Movement is a great success for Team GB and the game of Rugby at the Nanjing 2014 Youth Olympic Games, Rio 2016 Olympic Games and beyond."
Premiership Rugby chief executive Mark McCafferty believes Lancaster's background in developing elite players will stand him in good stead as England coach.
Lancaster worked with Corin Palmer, Premiership Rugby's head of academies and development, on the most recent investment in the national academy.
"Everyone involved in Aviva Premiership Rugby has known Stuart for many years and we have been fully aware of his outstanding abilities for some time," said McCafferty.
"He understands the mechanics of the professional game in England and has been involved in the infrastructure of our sport for many years. With Corin and our clubs he has been involved in the development of some of the best young players in England and that can only help in his role as England head coach.
"Stuart made a big impression on the Aviva Premiership clubs in his time as interim coach and we'd expect that relationship to grow now he has been given the job permanently. Our directors of rugby were very impressed with him, we are looking forward to working with him, and we wish him all the success in the future."
Lancaster described his appointment as England head coach as "an honour and a privilege" as he spelt out what he feels is needed for the team to claim World Cup glory on home soil in 2015.
Lancaster's appointment was confirmed today [Thursday] following a successful RBS 6 Nations campaign as interim manager where he led England to second place in the championship, helping to rebuild reputations after a disappointing World Cup showing under Martin Johnson last autumn.
His next task will be to lead England on a tough summer tour to South Africa, and he set out his blueprint for how England can move forward in the build-up to 2015.
"The two words that spring to mind are honour and privilege," he told a press conference televised by Sky Sports.
"Being head coach of your national team in any sport (is an honour), but to do it at a time when we've got a World Cup in our own country is a huge, huge honour.
"It's a very proud day for myself and my family, but it's not about me, it's about the team and the connection between the team and the English public.
"We had 82,000 people come to watch us Twickenham, there were 10 million people or thereabouts watching the Ireland game. England is a country that gets behind a team, there is no country that does that better than England."
Lancaster, who has worked his way up through grassroots coaching and is a former England Saxons coach, still works as assistant coach to the West Park Leeds under-11s team but his thoughts drifted last night to how he could take England to the top of the professional game.
"I was sat last night at West Park in Leeds having finished with the under-11s and we were talking about the tour - not the South Africa tour, the Scarborough tour," he said.
"I was sat there planning that and I thought 'what would I want to see if I was a mini-team rugby coach or a spectator?' and there are three things I'd like to bring to the (England) team.
"The first is pride, in wearing the shirt and the connection with people. The second is the vision for the future, and that is to win the World Cup in 2015. The third is for the players to play without fear, that when they come to play for England they can seize their opportunities and play without fear."
Rugby Football Union chief executive Ian Ritchie was not prepared to take questions on the make-up of Lancaster's support staff. Forwards coach Graham Rowntree is expected to remain part of the set-up but it remains to be seen if Andy Farrell, who was seconded to England for the Six Nations by Saracens, will join Lancaster's backroom staff on a permanent basis.
Lancaster added: "It's been everything that I've worked towards, going through all the coaching qualifications, it's what you strive for and it's a shot in the arm for all those people who believe in coaching.
"For me to get to the pinnacle it's an unbelievable honour."
Lancaster was given the full-time role on merit and being English did not favour him over other candidates, according to Ritchie.
"I don's see it (appointing Lancaster) as a gamble," said Ritchie.
"Stuart was given this job on merit against very strong competition.
"There were a large number of interested candidates in this job."
Despite his lack of international coaching experience - the Six Nations aside - Lancaster was the best man for the job, Ritchie said.
"He ticks all of the boxes that we need. We came back to the view that Stuart was the best candidate."
Asked if it was important that Lancaster was English, Ritchie said: "It's a bonus almost rather than a factor.
"To get the best candidate for the job was what we wanted, nationality was irrelevant."
Ritchie said the RFU felt Lancaster was well equipped to deliver at the World Cup.
"We appointed somebody who we felt would put us in the best place to be competitive to win the World Cup," he added.
"It's going to be very tough, the next series of matches in the autumn are against some very good teams."
Ritchie also rejected the suggestion Lancaster could have continued as interim coach.
"It's right to make the appointment now. We've got to move on," said Ritchie.
"It's been very interesting to see the support that Stuart has received and it's right that has been taken into account."