Former Liverpool youngster Amoo had his one-year contract at Deepdale terminated by mutual consent on Wednesday after making nine starts and 15 substitute appearances for Graham Westley's men, and the League One leaders moved quickly to secure the 21-year-old for the rest of the season.
Rovers boss Ronnie Moore said: "I'm really pleased to sign David. He's a player I tried to bring in last summer and one I'm excited to have at the club.
"He's got fantastic pace, he can beat players and he can score goals too. He can play out wide or up front and he gives us extra attacking options.
"I'm still hopeful of adding more new faces to the squad as well over the coming weeks."
Amoo added: "I'm happy to be here, it's a fantastic opportunity for me.
"I want to prove myself. The club is doing well and I want to help in the push for promotion."