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.

The 32-year-old former Charlton, Fulham, Chelsea and Bristol Academy player has been with Yeovil since 2015.
She netted seven goals in her first term for the Lady Glovers and a further seven in 2016 as Yeovil won WSL 2.
"I am so happy to be given another opportunity with Yeovil to play in WSL 1," Heatherson told the club website.
Phil Taylor set up a Premier League play-off semi-final with Peter Wright after claiming the last qualifying spot in Aberdeen.
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Yeovil Town Ladies forward Annie Heatherson has signed a new contract with the Women's Super League One club ahead of the 2017 WSL 1 Spring Series.