The 20-year-old, who failed to make a first-team appearance for United, spent the first half of the season on loan at Scottish Premiership side Motherwell.
Grimshaw, capable of playing in defence or midfield, is not immediately available as he requires minor surgery.
"This is a chance to get my career going," he told the club website.
"I have been at Manchester United a long time, but I am ready to move on and make a career for myself.
"It is great to be back home in Lancashire and I am looking to get settled and start to kick on with my career."
He joins Ben Pearson in moving from the Reds to the Lilywhites this month.
Find all the latest football transfers on our dedicated page.
Championship side Preston have signed versatile Manchester United youngster Liam Grimshaw for an undisclosed fee on a two-and-a-half-year deal.