The 31-year-old spent almost six years at the DW Stadium but for the last two seasons has been a fringe member of manager Roberto Martinez's first-team squad.
He will join up with Wednesday in July, joining a club newly promoted to the Championship, on a two-year contract.
Kirkland, who counts Coventry and Liverpool among his former clubs and won an England cap against Greece in 2006, said on his new club's website: "This is a fantastic move for me and I am delighted to be here.
"There have been stories about injuries but I have been fully fit for the last two seasons at Wigan and really frustrated at being a number two.
"I'm chomping at the bit to start playing again and to join a club like Sheffield Wednesday at this time is a great move, although there is great competition for places, which is great."
