The 22-year-old forward spent the second half of 2016-17 on loan at Rovers, making eight appearances.
Dunn had previous loan spells away from the Premier League club at Cheltenham Town, Burton Albion and Morecambe.
"I'm pleased to be able to bring a player of Jack's quality to the club on a permanent basis," said Rovers manager Micky Mellon.
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Jack Dunn has joined Tranmere Rovers on a one-year contract after he was released by Liverpool.