Taylor already knew he was through before his 7-5 win over Adrian Lewis as Dave Chisnall could only draw against James Wade.
Michael van Gerwen will meet Gary Anderson in next Thursday's other last-four match at London's O2 Arena.
Van Gerwen topped the table after beating Scotland's Anderson 7-4.
Fellow Scot Wright finished second to qualify for his first play-offs with a 7-1 victory over already-eliminated Raymond van Barneveld.
Taylor will go in search of his seventh Premier League crown buoyed by a convincing win over reigning champion Van Gerwen in week 14.
The Stoke thrower, 56, is retiring after the 2018 PDC World Championship concludes in January.
Dave Chisnall (Eng) 6-6 James Wade (Eng)
Phil Taylor (Eng) 7-5 Adrian Lewis (Eng)
Peter Wright (Sco) 7-1 Raymond van Barneveld (Ned)
Michael van Gerwen (Ned) 7-4 Gary Anderson (Sco)
There will be live text coverage of the semi-finals and final on Thursday on the BBC Sport website from 19:00 BST.
Phil Taylor set up a Premier League play-off semi-final with Peter Wright after claiming the last qualifying spot in Aberdeen.