The 21-year-old penned a five-year contract with the Old Trafford giants.
The pacey winger scored five goals and offered 10 assists in 38 appearances in all competitions.
Speaking about the move, the Premier League club released an official statement via their club website on Friday, and it reads:
Manchester United is delighted to announce that it has agreed, in principle, terms with both Swansea City and Daniel James for his transfer to the club
Daniel has successfully completed a medical at the Aon Training Complex. Further details will be communicated once the international transfer window opens next week.
James becomes Ole Gunnar Solskjaer’s first signing since his arrival as manager in December 2018.