Scotland international Fletcher, 29, who finished last season on loan with French club Marseille, has agreed a four-year deal with Wednesday.
The centre forward has been linked with a move to Celtic since the January window, though the Parkhead club will be consoled with the signing of Moussa Dembele from Fulham on Tuesday.
“Sheffield Wednesday have signed international striker Steven Fletcher,” the Sky Bet Championship club announced on their official website.
“The Scotland star joins the Owls on a free and has put pen to paper on a four-year contract.”
Fletcher started out in Scotland with Hibernian and was signed for £3million by Burnley in the summer of 2009.
He scored 12 goals in 38 appearances for Burnley before moving on to Wolves in a £6.5million deal the following summer and commanded a £12million fee when he signed for Sunderland in August 2012. The Scot scored 23 goals in a total of 108 appearances for the Black Cats.
Fletcher has 28 senior international caps and is one of only five players to have scored three hat-tricks for Scotland.
Sunderland released Fletcher, plus Danny Graham, Wes Brown and goalkeeper Steve Harper earlier this month.