Agyemang, who has scored three goals this season, is set to go straight into the Robins' squad for Tuesday night's visit of Cardiff, subject to Football League approval.
He has made 61 appearances for Rangers, scoring 14 goals.
It is being widely reported that Leicester City are the favourites to sign Manchester City striker Kelechi Iheanacho, and if
Last week Wayne Rooney completed his return to boyhood club Everton, writing the final chapter in a fairy tale career.
Wayne Rooney has returned to Everton after 13 years at Manchester United.
Germany defender Antonio Rudiger has joined Chelsea from Roma on a five-year contract.
Wayne Rooney has closed the chapter on a Manchester United career that featured a raft of honours across 13 years.
Wayne Rooney has returned to Everton after a record-breaking career at Manchester United.