According to Sky Sports News, James will undergo a medical today and is likey to be announced as a United player imminently.
The 21-year-old reportedly attracted interest from numerous Premier League clubs, but it was United who moved first.
It's thought that James will cost £15 million with an extra £3m in add-ons.
The youngster enjoyed a fine campaign in the Championship for a middling Swans side, scoring four goals and grabbing seven assists from his position on the left wing.
In January he almost joined Marcelo Bielsa's Leeds United for £10m, having completed a medical, only for his deadline-day move to collapse at the last minute after a late disagreement between the two clubs.
Instead, however, it looks like he will get a dream move to Old Trafford only five months later.
James is currently part of Ryan Giggs's Wales squad and will return once his move is completed, as the Dragons prepare to face Croatia in a Euro 2020 qualifier.
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