Former Barcelona goalkeeper Victor Valdes is training with Manchester United as he recovers from a serious knee injury.
Crystal Palace defenders Damien Delaney and Joel Ward have yet to agree new deals at the club.
The 20-year-old joined the Owls over the summer and has already made nine appearances for Dave Jones' side.
Rangers chief executive Charles Green said: "Rangers and Sheffield Wednesday have agreed terms over Rhys McCabe.
"Sheffield Wednesday have acted in good faith and recognised our rights as a club during the process.
"We wish them every success this season and beyond and while we were disappointed Rhys decided his future lies away from Rangers we wish him well for the future."