The 20-year-old failed to make a single first-team appearance for the Red Devils and spent the first half of this season on loan with Motherwell.
Able to play in midifield or defence, Grimshaw becomes the third United player to move to Deepdale in January after Ben Pearson completed a permanent move and goalkeeper Sam Johnstone joined on loan.
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"I have been at Manchester United a long time, but I am ready to move on and make a career for myself," he told Preston's official website.
"This is a chance to get my career going. It is great to be back home in Lancashire and I am looking to get settled and start to kick on with my career."