The Welsh winger completed his £15m Old Trafford move on Wednesday, and could see his transfer fee rise to £18m due to add-ons.
James isn’t the only young wide player to be the subject of transfer speculation this summer, as Liverpool face their own battle to keep Ryan Kent.
The 22-year-old spent last season on loan at Rangers but is not keen on another temporary move away this summer.
Kent will now either stay at Liverpool and fight for his place in the first-team – or will be offloaded for a fee of around £12m.
The Reds are said to have decided that figure as a result of James’ own transfer fee, according to Goal.
Rangers are reportedly unwilling to pay the £12m Liverpool are looking for, but Aston Villa and Middlesbrough are keen to make respective bids.
Leeds have made a move for Kent but were only willing to launch a loan bid.
James’ transfer means he is the first of Ole Gunnar Solskjaer’s reign at the club.
Speaking today, the United boss said: “Daniel is an exciting young winger with lots of skills, vision, exceptional pace and a good work ethic,” he told United’s official website.
“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 added: “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.”