Jose Mourinho's side needed three points to claim the trophy with three games to spare and Eden Hazard headed in the rebound after missing a first-half penalty.
Mourinho's 21st trophy of his prolific career was the Capital One Cup win at Wembley in March -- the first of his second spell at Stamford Bridge -- and now the Portuguese has a third Premier League title and Chelsea's fourth in 11 seasons.
The self-proclaimed Special One delivered the first title 10 years ago -- the 2004-05 win was Chelsea's first championship in 50 years -- but domestic league success has eluded the Blues since Carlo Ancelotti led them to the 2009-10 title.
Chelsea entered Sunday's fixtures 13 points clear of Manchester City and Arsenal, the only team who could overhaul them as they have a game in hand.
City, despite giving up ther crown were back to their best as a Sergio Aguero goal gave them a 1-0 win at White Hart Lane that puts them second, but Arsenal now have two games in hand on the Manchester side.
Both sides seem certain of Champions League football though as manchester United's defeat to West Brom was the first time in 15 years they have lost three on the bounce in the league.