On a historic afternoon on Centre Court, Murray defeated Novak Djokovic 6-4 7-5 6-4 to become the first home male champion at SW19 since Fred Perry claimed the title in 1936.
Buckingham Palace said the Queen sent a private message to the Scot following his victory, which came with the backing of a buoyant crowd.
A Buckingham Palace spokeswoman said: ''I can confirm that the Queen has sent a private message to Andy Murray following his Wimbledon victory.''
A host of politicians from either side of Hadrian's Wall gathered in the Royal Box to cheer Murray on, including Prime Minister David Cameron.
''It was fantastic, it was an absolutely brilliant performance, an amazing day for Andy Murray but also an incredible day for British tennis and for Britain,'' he told BBC News.
''He's an amazing player but what he showed today [Sunday] is not only how brilliant he is technically but also he's got this incredible courage.
''You are playing against Djokovic, who's the great artist of comebacks and never gives up and Murray just kept going.
''He was magnificent.
''It felt like the Olympics, it felt like one of those moments when the whole country is watching and there is just an amazing sportsman who's dedicated his life and had wanted to win so badly and then just producing a performance that was exquisite.''
Other politicians joined the Prime Minister in congratulating Murray.
Scottish first minister Alex Salmond, who was also in the Royal Box and unfurled a Saltire after the match ended, said it was a ''truly phenomenal victory''.
''Andy's determination to win was visible in every point and he delivered an outstanding result in a real clash of tennis titans,'' he said.
''His phenomenal performance against the world number one displayed incredible physical prowess and depths of mental fortitude.
''The shouts of ''Come on Andy'' were ringing all the way from Dunblane to SW19.
''Last year Andy Murray won the hearts of Wimbledon, this year he has won the championship and on today's form there will be many more victories to come.
''Novak Djokovic displayed typical grace and sportsmanship in defeat. But Andy has firmly secured his place in Scottish sporting folklore.
''He is one of the greats of the game and his success today will inspire a new generation of tennis champions.''
Former British number one Tim Henman backed Murray, who also won the US Open last year, to go on and win more grand slams.
''It's a remarkable achievement for him and something we are proud of,'' Henman said.
''Andy had this belief in his heart of hearts that he would win it.
''He had some huge disappointment with losing 12 months ago but deep down he knew he could do this and this is going to be one of many more grand slams for Andy Murray.''
Mats Wilander, the Swede who won seven grand slam titles in the 1980s, believes Murray could be on course for a big haul.
Wilander said on Live@Wimbledon: ''I think Andy Murray can win six, seven, eight, nine, 10 majors.
''The only man that can stop him is Novak Djokovic.
''These two here are going to decide who gets ahead in the history books.
''I hope they both decide this is a rivalry that's just going to grow and become great on all the different surfaces, in all four majors.''
Roger Draper, the chief executive of the Lawn Tennis Association, said Murray's victory was the best British tennis has ever known.
Draper, who leaves the LTA in September, said: ''Andy has provided British tennis with its finest moment, on the world's greatest tennis stage.
''Just as he did last year, at the Olympics and US Open, Andy has proved himself to be an inspirational role model, and he has given British tennis a fantastic opportunity to get more people playing tennis.''