Kirkland agrees Wednesday move
The former England international has ended his six-year association with the Latics and is now keen to push for regular first-team football with the Owls.
Kirkland, 31, fell behind Ali-Al Habsi in the pecking order under Roberto Martinez but claims his recent lack of action is not due to fitness problems.
The former Coventry and Liverpool shot-stopper will be hoping to help Dave Jones' side establish themselves in the Championship after securing promotion on the final day of the League One season.
Kirkland told the club's official 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 No.2.
"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.
"Everybody saw what happened at Hillsborough on the last day of the season and to think that I will be part of that is really exciting."
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