The 18-year-old progressed through Rovers' youth ranks to make his first-team debut in August's Johnstone's Paint Trophy meeting with Port Vale, going on to make four further first-team appearances.
Power is yet to feature since Ronnie Moore replaced Les Parry as manager in March, but the Prenton Park boss has been impressed by the youngster's efforts at reserve level.
"Max is a hard working young midfielder who deserves this new contract," said Moore in a club statement. "He's done well for the reserves and if he continues to progress he can compete for a place in the first team next season."
Power added: "I'd like to thank the gaffer for giving me this opportunity.
"I've had a taste of the first team this season and I enjoyed it. I'm going to do everything I can to be involved as often as possible next season."