The 19-year-old has featured in Premier League and Champions League games for City, as well as representing the England Under-20 team.
He arrives at Deepdale having spent the first part of this season on loan with fellow Championship side Stoke, where he scored three goals, and could make his debut for the Lilywhites against Norwich on Saturday.
Delap told the Preston website: "I'm buzzing. It's such a great club and I'm really excited to meet the boys and play in front of the fans.
"I've spoken to the manager and I'm really happy with what he's got to say and the style of football he plays, so I can't wait to get playing under him.
"As a striker at the end of the day, the manager wants goals so that's what he's said to me.
"I trust myself in front of goal. I trust myself to get in the right positions so if I get the opportunity then hopefully I can bring that."
Manager Ryan Lowe added: "Liam was one we targeted in the summer because of the work he'd done with City's U23s and he had some input in the first team with a couple of goals, too.
"With him being called back now we felt it was important to make our move and I'm really pleased we've got it over the line.
"He's a good lad, a good footballer and a goalscorer. He just needs an opportunity to score goals and hopefully we can give him that.
"Obviously we're going to be without Emil [Riis] for a long period now too, so we felt we needed to bring an extra body into the building to continue the form we've had."