This online news platform understands that James signed a five-year contract, with an option to extend for a further year.
The Wales international made his professional debut for Swansea City in February 2018 and his senior Wales debut in November 2018, having previously represented the nation at various youth levels.
It was gathered that the 21-year-old signed for United at the Aon Training Complex.
United boss Ole Gunnar Solskjaer said: “Daniel is an exciting young winger with lots of skills, vision, exceptional pace and a good work ethic. 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.”
James, on his part, said, “this is one of the best days of my life and a challenge I am really looking forward to. The Premier League is the best league in the world and Manchester United is the perfect place for me to continue to develop as a player.
“This is an incredibly proud moment for me and my family; however, it is tinged with sadness that my father isn’t able to share this experience with us. I am looking forward to working with Ole, meeting the team and getting started.”