Harrop finished as United's top goalscorer at Under-23 level last season and marked his senior debut with a stunning goal against Crystal Palace on the final day of the 2016-17 campaign.
He will sign a four-year deal at Deepdale, with the two clubs agreeing on an undisclosed compensation fee.
“I'm delighted to be here, it's a new start for me to get things going in my career and I'm buzzing to get playing and to make an impact in the team," Harrop said in a club statement.
“Hopefully I can achieve my aims and ambitions that I have set myself by coming here and that's to get promoted with Preston North End and help the club get as high as we can."
Harrop will link up with former United team-mates Marnick Vermijl, Ben Pearson and Liam Grimshaw at Preston ahead of the 2017-18 Championship season.
Speaking of the deal, Preston manager Simon Grayson said: "Josh is a player who has attracted a lot of interest this summer and we had to move quickly to secure his signature.
"He adds to our group of hungry young players who want to progress and we are looking forward to working with him and seeing him improve."