The 28-year-old has signed a one-year contract with Rovers, who were relegated to the Conference in May.
Tranmere boss Gary Brabin told his club’s official website: “I’m delighted to bring Scott to the club. He’s a good character and an excellent goalkeeper.
“He’s hard-working and possesses a great attitude, plus he knows this league and the one above really well so he’s a welcome addition to the squad.”
Davies, who started out at Morecambe, made 170 appearances for Fleetwood after joining them in 2010 and has also had loan spells at Morecambe and Accrington.