Substitute Michy Batshuayi scored in the 82nd minute to secure the vital win, sliding in to turn home Cesar Azpilicueta's cut-back from close range.
After nearest rivals Tottenham lost against West Ham on 5 May, Chelsea needed only two wins from their final four matches to take the trophy.
They convincingly beat Middlesbrough 3-0 on Monday and wrapped things up with victory at The Hawthorns.
Chelsea were made to work hard on the night by a resolute West Brom.
The Blues had 14 shots on goal in the first half, including Cesc Fabregas' bending effort which went wide.
Victor Moses struck through the legs of James McClean, only to be denied by a brilliant save from Ben Foster after the break.
West Brom took control of the match, as Salomon Rondon's shot deflected wide after a rapid counter-attack and Nacer Chadli clipped his effort past the post.
But then Batshuayi scored his second league goal of the season, sending the Chelsea players and manager Antonio Conte into frenzied celebrations.
Conte becomes only the fourth manager to lift the Premier League trophy in his first season in England, emulating Jose Mourinho in 2004-05, Carlo Ancelotti in 2009-10 and Manuel Pellegrini in 2013-14.
And the Italian has claimed a fourth successive league title as a manager - adding to the three Serie A trophies he won with Juventus.
Story & Picture Credits: BBCBLOG COMMENTS POWERED BY DISQUS