Ridehalgh, 22, made 18 appearances for Rovers during his three-month loan spell and has now joined on a permanent basis.
He told the club's official website: "I'm really happy to be here and glad everything is sorted.
"The loan finished on December 29 and I got a phone call saying Tranmere wanted to sign me permanently and I was really happy with that.
"I think Tranmere is a good club, I'm settled here and I want to kick on now."
- Sports & Recreation