Sources told ESPN on Aug. 30 that the two clubs were discussing a move for the 23-year-old.
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The winger will move to Elland Road after his transfer was completed on deadline day.
James started two of United’s first three games of the season but has secured a move away from Old Trafford after concerns about his prospects under Ole Gunnar Solskjaer following the arrivals of Jadon Sancho and Cristiano Ronaldo this summer.
James joined United from Swansea City in a deal worth £15m rising to £18m in 2019.
He has made 74 appearances for the club, scoring nine goals.
Leeds are long-term admirers of James and almost signed the Wales international before he moved to Old Trafford. He was on the brink of joining Leeds from Swansea in January 2019 before the move collapsed at the last minute.