The 21-year-old became the first arrival of the Ole Gunnar Solskjaer era at the 20-time English champions after Manchester United confirmed the transfer on Wednesday night.
James is reported to have cost £15m to sign from Championship side Swansea City after his impressive performances throughout the 2018-19 season in the second tier.
Wales manager Giggs gave James his big break in the national team, which spurred the attacking midfielder to go on and cement a regular place in the Swansea side.
Asked about the role that Giggs played in his transfer to the 20-time English champions, James told the club’s website:
“Ryan was obviously a big credit to why I’m here now.
“Obviously he gave that opportunity to me in the Slovakia game, and to score in the first five minutes was amazing for me.
“I think the trust he’s given me, and from then on he’s watched a few games of me at Swansea… he’s a big credit to why I’m here now.
“Obviously he mentioned me here and I’d give a lot back to him for that.”
James netted five times in 38 games for the Welsh side last season following a loan spell at Shrewsbury Town in the 2017-18 campaign.
The Manchester United summer signing made his debut for Wales against Albania in November 2018.
James scored his first international goal and Wales’ winner in their 1-0 victory over Slovakia on his competitive home debut at the Millennium Stadium in back in March.
Manchester United finished in sixth place in the Premier League table last season to miss out on a spot in the Champions League.
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