Power has scored three times in 22 appearances for Rovers this season and his new deal runs until June 2015.
Manager Ronnie Moore told the club's official website: "Max has progressed really well this season. He's played a lot more than he would have expected after the injury of James Wallace and he has made the most of his opportunity.
"It is a big step up from reserve team football to playing regularly in League One but Max has impressed me. He's learning each match and if he continues to work hard he can be a very important player for Tranmere Rovers.
"He's scored a couple of fantastic goals for us already this season and hopefully there are one or two more to come from him in the final 10 games."
Power added: "I'm really happy to have signed my new contract. I love it here at Tranmere and it has been great to be regularly involved with the first team this season.
"Now I want to do everything I can to help the club finish in the top six this season. We've got 10 massive games left and we'll give it our all in every one of them."