The 20-year-old has yet to feature for the first team at Anfield, but has impressed while on loan at Accrington Stanley and Hartlepool United.
Ronnie Moore, the Rovers boss, revealed the youngster has been a long-term target for his side.
"Godwin is a very talented young defender who we've been watching for some time," he said.
"He has spent the last three seasons at Liverpool so has worked with some great coaches.
"He is comfortable on the ball, already has Football League experience from his time at Hartlepool and he will add quality, strength and pace to our defence."