After loan spells with Shrewsbury and Cheltenham, the 19-year-old spent the last seven weeks of the season at Prenton Park helping Rovers avoid relegation from League One.
And Albion have on Friday revealed they will not be taking up their one-year option on Labadie's contract, leaving him free to part ways with the Black Country club after four years at The Hawthorns.
Tranmere manager Les Parry on Wednesday said: "We've made Joss an offer and hopefully we can keep him."