Manuel Pellegrini’s side knew that a victory would seal their second title in three years regardless of what happened in Liverpool’s match against Newcastle.
Samir Nasri settled the nerves when he opened the scoring for the hosts with just six minutes remaining of the first half.
Captain Vincent Kompany then slotted home from close range shortly after the re-start to end any danger of City not winning the title.
Liverpool came from one goal down to beat Newcastle, but following City’s comfortable win, it was not enough to end their title drought which will now stretch into a 25th year.
Nasri said: “It’s an amazing feeling. My second title in three years. It was an amazing league the whole year. There are no words to explain the feeling now. Maybe in an hour or two we will feel it. I’m so happy for the manager too because it’s his first title in England.
“He remained calm all season for us to play attractive football and it was a pleasure to work with him. The Liverpool game against Chelsea, I think that was the twist of the season.”
At Anfield, an own-goal from Martin Skrtel put Newcastle ahead in the first half, but Daniel Agger and Daniel Sturridge scored to give the Reds a bittersweet victory.
Chelsea had to settle for third place after coming from a goal down to win 2-1 at Cardiff City, ending a trophyless first season back in England for manager Jose Mourinho.
Tottenham Hotspur beat Aston Villa 3-0 to finish sixth and clinch a place in next season’s Europa League, meaning Manchester United, who drew their final match 1-1 against Southampton, will not play in Europe next season for the first time in 24 years.
Norwich City’s relegation was confirmed with a 2-0 home defeat by Arsenal and they will join Cardiff and Fulham in the Championship next season.