The 20-year-old, who can play out wide or up front, has emerged as one of the brightest young talents at United, and was handed his debut by then interim boss Ryan Giggs at the end of last season having impressed during earlier loan stints at Yeovil and Carlisle.
His previous deal expired this summer, and United had been locked in talks to try and keep him at the club as Sky Sports understands more than a dozen clubs from the Premier League and Championship were interested in acquiring his services.
Welsh clubs Swansea and Cardiff tried to sign Lawrence back in January and their interest is known to remain, while the likes of Southampton, Newcastle, Sunderland, Leicester, Burnley, Stoke, Blackburn and Norwich have also showed an interest.
But Lawrence looks to have pledged his future to the Red Devils, with the hope of making the breakthrough under Louis van Gaal in the coming season.
Lawrence was also handed a call-up by Wales over the summer, but while his club future is set to be resolved, his international one is far from decided.
Sky Sports understands that, despite his call-up, England youth supremo Gareth Southgate is looking very closely at Lawrence, who would qualify through his English father, with a view to persuading him to make the switch.