On the final day of the January transfer window, Rovers moved to secure the defender on loan until the end of the season, but they were unable to confirm a deal with the Nigerian needing to be granted a work permit.
However, almost a month since he first began training with Rovers, he has now been ordered to go back to Glasgow after the application was turned down.
Rovers boss Tony Mowbray told the Lancashire Telegraph: "The club has worked very hard behind the scenes to try and make it happen, but it's not going to be happening.
"I spoke to the boy, I enjoyed his company as a football guy, he understood the situation and percentage wise it proved very difficult for us to get a work permit for him.
"It could have taken five, six or seven weeks which would have taken a lot of games out. Whether we address that later on we will wait and see."
Ambrose has not featured in the first team at Celtic since July 27.