Grant, 19, has penned a two-year contract at Glanford Park, with the Iron having the option to extend it by a further season.
He is out-of-contract at Stanley, but as he is under the age of 24 a transfer fee will be paid. The amount has not been agreed between the clubs, a transfer tribunal will decide the price if an agreement cannot be made.
"It's a great opportunity for me, playing in the Championship. This is a fresh start and hopefully I can perform now for Scunthorpe," he told the Iron's official website.
"I just want to get into the team and perform well at such a high stage."