The 21-year-old shone while on loan at Shrewsbury last term, playing a key role as they reached the League Two play-off final.
He saved two penalties in the semi-final shoot-out victory over Bury.
He has signed a new contract to stay with Albion and will look to gain more first-team experience at Prenton Park.
Tranmere manager John Barnes said: "I'm pleased to be able to bring a young goalkeeper of Luke's quality to Tranmere.
"He had a very impressive season at Shrewsbury and has a good future ahead of him. I'd like to thank West Brom manager Roberto Di Matteo for allowing Luke to join us on loan."