James will be the first new arrival of the summer at Old Trafford and the first signing for new manager Ole Gunnar Solskjaer, after both Swansea and United announced the transfer on Friday.
The 21-year-old represents a new direction for United in terms of transfer policy, with the club seemingly trying to target young domestic talent instead of established overseas stars.
United said in a statement: "
"Daniel has successfully completed a medical at the Aon Training Complex. Further details will be communicated once the international transfer window opens next week."
We're delighted to have agreed terms, in principle, with Swansea City for the transfer of Daniel James to #MUFC.— Manchester United (@ManUtd) June 7, 2019
Further details will be revealed in due course.
Swansea, in a statement of their own, indicated that the transfer will be made official on Tuesday, when the international transfer window opens.
James will likely report for pre-season training with the rest of his new teammates and his first action in a United shirt could be the friendly in Australia against Perth Glory on 13 July.
The player is currently on international duty with Wales, and featured for them on Saturday in a match with Croatia.