It is understood a fee of £13.5million, plus £1.8million in potential add-ons, had been agreed with the Portuguese club over the weekend for the left-back, whose deal includes the option to extend for a further year.
He said on the club website: “To join a club with the prestige of Manchester United is a huge honour.
“You have to work hard to get to this moment in your career and now I am coming to this club, I can promise that I will give everything in my heart to be a success here.”
There could be more business done by the Old Trafford club before the end of transfer deadline day.
Former PSG striker, Edinson Cavani, is set to sign on a free contract and United are still in the market for a right winger, although their quest for Jadon Sancho looks dead in the water.
