The forward, who volunteered to take a pay cut to help the administration-hit Jambos last summer, quit the Edinburgh club last week after rejecting another wage cut.
He has now penned an initial two-year deal with Alan Archibald's side, with an option for a third built into his contract, as revealed in later editions of SportTimes yesterday.
The former Chelsea youth-team player joined St Johnstone in 2002 before returning to home-town club Ayr United.
It was after three years at Somerset Park that he joined Hearts for the first time.
A six-month stint at Ipswich interrupted his time at Gorgie before he returned 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.