"I'm really happy to have signed. I just want to get started now and play some games," said 19 year-old Barnett.
Manager Ronnie Moore added: "This is a brilliant signing for the Club and it's one I'm very excited about. Charlie has done really well in pre-season with us.
"He has all the Liverpool traditions - he's got great touch, vision and technique. He'll bring a touch of artistry to the side and I'm sure he'll go a long way in the game, hopefully with Tranmere.
"It's nice to see the growing links between Tranmere and Liverpool. The friendly against them was a great day for football on Merseyside and we've since signed two of their players.
"It's a good opportunity for any Wirral based Liverpool supporters to come to Prenton Park and watch some of their talented youngsters in action for Tranmere."