Substitute Michy Batshuayi prodded home Cesar Azpilicueta’s shot-cross from close range in the 82nd minute to see the Blues pass a dogged West Brom side that looked to be in the ascendancy in the second period.
Victory gives Antonio Conte’s men an unassailable 10-point lead with three games left to play for the closest title contenders Tottenham Hotspurs, and this represents a remarkable turnaround from last season that saw them finish 10th.
Chelsea came into the tie needing only two wins from their final four matches to take the trophy after Spurs lost against West Ham on 5 May.
They dispatched Middlesbrough 3-0 on Monday, but were made to work hard for tonight’s decisive victory at the Hawthorns.
The Blues dominated the opening half but were kept at bay by a resolute Baggies side that had goalkeeper Ben Foster on inspired form.
West Brom then grew into the tie, with Salomon Rondon and Nacer Chadli missing good chances to break the deadlock.
With his side struggling for inspiration, Conte made a double substitution, throwing on Willian and Batshuayi for Eden Hazard and Pedro, and it yielded the required result as the Belgian striker bundled home his second league goal of the season to send the Chelsea contingent into wild celebration.
Conte, 46, becomes only the fourth manager to lift the Premier League trophy in his first season in England, joining Jose Mourinho, Carlo Ancelotti and Manuel Pellegrini.