Bradley fired a final-round six-under par 64 at Aronimink Golf Club to match Rose on 20-under par 260, then took advantage of the Englishman’s bogey at the par-4 18th on the first playoff hole for his fourth career tour victory.
Bradley, the 2011 PGA Championship winner, had not won a title since the 2012 WGC Bridgestone Invitational. He won the 2011 PGA and his first title, the 2011 Byron Nelson Championship, in playoffs as well.
Rose settled for solo second but it was still enough to lift him from fourth in the rankings to world number one, overtaking Dustin Johnson for the top spot.
The 38-year-old Briton became the fourth English man to capture the top ranking after Nick Faldo, Lee Westwood and Luke Donald. Rose became the third oldest among 22 to hold the top spot.
Americans Billy Horschel and Xander Schauffele shared third, one stroke off the pace, with Rory McIlroy fifth on 262 and 14-time major winner Tiger Woods sharing sixth after a closing 65 on 263 alongside US Ryder Cup teammate Webb Simpson.
© Agence France-Presse