Robins boss Lee Johnson has already signed Everton midfielder Liam Walsh in the January transfer window.
Jamie Murphy was poised to make a move to Bristol City before Rangers sealed his signature.
According to a report in the Scottish Sun, the Robins were willing to fork out £1.8m for the Brighton and Hove Albion winger but the Seagulls realised how much he wanted to return home and instead let him go back to Scotland.
The former Sheffield United and Motherwell player has initially moved to Rangers on loan but will make the move permanent in the summer when a price for the 28-year-old is agreed.
After securing a move to Ibrox, manager Graeme Murty said: “We hope he’s going to be able to replicate the kind of form that made him a mainstay in the Brighton team last season, a player that was so vital in their successful push for promotion to the Premiership.