Waring, 22, played under Rovers manager Micky Mellon at League One Shrewsbury last season during a loan spell.
He spent the second half of the season with Carlisle, helping the Cumbrians reach the League Two play-offs.
"I enjoyed working with George at Shrewsbury and know the qualities he will bring to the group," Mellon said.
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National League side Tranmere Rovers have signed striker George Waring on a two-year deal following his release by Stoke City.