Celtic appear to have missed out on signing Manchester City striker John Guidetti after failing to beat the deadline.
Jermain Defoe came close to returning to England on deadline day, but Toronto FC are hoping to keep him long-term.
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."