Pep Guardiola's side moved an insurmountable 16 points clear of United with five matches remaining, thanks to Jay Rodriguez's header in the 72nd minute.
Guardiola, who becomes the first Spanish manager to win the Premier League, has now won a remarkable 24 trophies in his nine-year management career.
He is the third Manchester City manager to claim the English title, after Roberto Mancini, in 2011-12, and Manuel Pellegrini, in 2013-14.
City have dominated this season, racking up 87 points after winning 28, drawing three and losing just two of their 33 fixtures so far.
They are eight points adrift of the Premier League record for points in a season, Chelsea's 95 in 2004-05, and can become the first team to break the 100-point barrier, with a total of 102 possible from their remaining five matches.
Guardiola said he is proud to Manchester City manager and believes his players have been "awesome" this season en route to winning the title with five games to spare.
"It's incredible the way we played and I am so glad to be here and be part of this club," he said after the 3-1 win over Spurs at Wembley.
"These guys are fantastic, awesome - they are incredible. This club is absolutely amazing in all terms."
Captain Vincent Kompany, in his 10th campaign with the Blues and now officially the most successful captain of all time, dedicated the crown to the City fans.
"As much as this has been a record breaking season, this one's for you, the fans, this is why we do it!" said the skipper.
Kompany, at home in Manchester, revealed many of his team-mates had flown off for mini-breaks to see family and friends after being given three days off.
He said: "There's players all over the world Portugal, Spain - you name it - wherever. We didn't expect this, we've been Facetiming, talking on the chat and everyone is in touch and as much as we're far away from each other at this moment in time, we are still very close, and we will somehow spend the night celebrating together.
"Today is a sense of achievement because we've won the title in a way for the first time, I'd like to have won all other titles, so I'm extremely proud about this, and extremely aware of how fast these moments can go."
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