The Rugby Football Union are expected to confirm the announcement at a press conference on Thursday afternoon.
Lancaster's permanent appointment follows a 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 saw off competition from former South Africa and Italy coach Nick Mallett to be proposed for the job by Ian Ritchie, the RFU's new chief executive who oversaw the recruitment process.
Ritchie was assisted by an advisory panel comprising Conor O'Shea and Ian McGeechan - the Harlequins and Bath directors of rugby respectively - the RFU's professional rugby director Rob Andrew and former England flanker Richard Hill.
Lancaster's appointment was ratified, it is understood, by the RFU board in a conference call on Wednesday night. He will now lead England to the World Cup in 2015.
There was no word on whether Andy Farrell, who was part of Lancaster's interim management team during the Six Nations, will be joining the full-time coaching team.
Farrell remains under contract at Saracens, who said on Wednesday there had been no official approach from the RFU.
Lancaster, a former Leeds director of rugby, was in charge of the England Saxons and elite player development at the RFU when he took over the national team after Martin Johnson stood down.
England had crashed out of the World Cup in the quarter-finals and the subsequent leaked reports indicated a squad riven by distrust and competing agendas.
Lancaster rebuilt the England team and they won four of their five matches in the Six Nations, including a victory over World Cup finalists France in Paris and a 30-9 thumping of Ireland at Twickenham.
The former school teacher would not have been deemed a realistic candidate for the permanent job when he took the reins in December and the RFU had already contacted Mallett.
But his efforts in restoring the reputation of English rugby following a World Cup campaign dogged by controversy won him immediate admirers within Twickenham.
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.
He 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.
After the Six Nations, Lancaster delivered a presentation on his vision for how England would win the World Cup in 2015 and he made a case in his interview for the development of a national centre of excellence.