The 29-year-old volunteered take a pay cut to help the administration-hit Jambos last summer, but rejected another attempt to slash his wages even further.
He has now put pen to paper an initial two-year deal at Firhill, with an option for a third built into his contract.
The former Chelsea youth-team graduate joined St Johnstone in 2002 before returning to home-town club Ayr United in 2007.
After three years at Somerset Park he moved to Hearts for the first time, but then had a six-month stint in England with Ipswich Town before returning to Tynecastle in August 2012.
However, having taken reduced salary payments last season, Stevenson decided to move on when Hearts' relegation to the Scottish Championship meant they had to trim back his contract terms even further.