James’ transfer fee is said to be an initial £15m, which could rise to £18m due to add-ons.
The deal is Ole Gunnar Solskjaer’s first as United manager.
The Red Devils look set to splash even more cash in the coming weeks – but who will be joining James at Carrington before the August deadline?
One man heavily linked with a move to United is Sporting Lisbon star Bruno Fernandes.
Portuguese outlet Jornal de Noticias last week claimed the Red Devils had offered an initial €55m (£48m) plus a further €25m (£22.2m) in bonuses for the player.
Fernandes is now enjoying a well-deserved rest following his country’s Nations League triumph.
Tottenham are also plotting to sign the midfielder, who was Sporting’s player of the season this term.
United also remain in the hunt for Matthijs de Ligt.
The Red Devils have been heavily linked with the Dutch starlet, despite interest from PSG, Barcelona and Liverpool.
De Ligt recently admitted he was unsure over his next destination.
But his agent Mino Raiola has previous when it comes to doing deals with United, due to his representation of Paul Pogba and formerly Romelu Lukaku.
Solskjaer is keen to shore up his defence this summer.
Starsport understands another defender that could move to Old Trafford is Benfica’s Ruben Dias.
The 22-year-old is seen as a cheaper alternative to Napoli’s Kalidou Kouliably, who is valued at around £150m.
Dias would only set United back around £50m.
The Portuguese defender also won the Nations League at the weekend.
As for James, Solskjaer is certainly delighted with his first signing of the summer.
“Daniel is an exciting young winger with lots of skills, vision, exceptional pace and a good work ethic,” he told United’s official website.
“He had a great season with Swansea City and has all the attributes needed to become a Manchester United player.
“We are delighted he has signed with our club and we are all looking forward to working with him.
“This is the perfect environment for Daniel to continue his development.”