The 22-year-old has put pen to paper on a two-year deal to become manager Greg Abbott's first summer signing.
"David fits the bill of the type of player we want to bring into the squad," Abbott told the club's official website.
"He's quick and exciting on the ball and we think he'll bring a bit of the pace and flair we've been talking about.
"The important thing for us is that he wants to play football. He's at an age where he's ready to kick on and, hopefully, that's exactly what will happen here with us.
"He's one we're really looking forward to working with."
Amoo, born in London, started his career at Millwall before being signed by Liverpool at the age of 16.
He had loan spells at MK Dons, Hull, Bury and Preston during his time at Anfield and signed a permanent deal at Deepdale in July last year.
Amoo joined Tranmere on a six-month deal in January and scored one goal in his 11 appearances for Ronnie Moore's side.