Boss Neil Warnock told the QPR website: "Some people might be surprised by this signing but he's a player I've fancied for a very long while."
Clarke joined Wednesday in January 2007 and scored 18 goals in 83 league games.
Warnock added: "I think he's got a lot of ability, but I think he's underachieved. I rate him very highly though."
Clarke, who played one game on loan at QPR earlier in his career, said: "Neil has outlined his plans for the campaign and it promises to be an exciting chapter in the club's history."