Manchester United boss Ole Gunnar Solskjaer signed James for an initial £15m from Swansea last month.
He signed a five-year deal at Old Trafford and became Solskjaer’s first signing since he became the club’s manager.
After James completed his move to the north west, his international manager Giggs congratulated him on the move.
The Wales boss told the winger to simply be himself, and his quality would ultimately tell.
“The way [Giggs] brought me and a lot of other youngsters through has been amazing,” said James.
“He spoke to me when I first signed for United. His advice was to be myself, which is what I will try to do.
“He wasn’t a bad player was he? What he did at Manchester United was amazing.
“Every young winger looks up to a person like him. He was playing in the Premier League until he was 40 and he was still beating players.
“Credit to him, the way he looks after his body. It is amazing for me, when I go away on internationals, to learn from people like him. He is obviously someone I aspire to be like.”
Giggs handed James his first international cap with Wales in November.
But, he said that signing for United was one of the best days of his life, and a challenge he’s really looking forward to.
The 21-year-old said Old Trafford is the perfect place for him to continue developing as a player.
James scored five goals last season with Swansea, as well as recording 10 assists.
He was the exact type of player that Solskjaer wanted to recruit to the club this summer, as the Norwegian targets young talent.
Meanwhile, United have also confirmed the signing of Crystal Palace right-back Aaron Wan-Bissaka for £50m.
They’re reported to be close to agreeing deals for Sporting Lisbon’s Bruno Fernandes, and Leicester City’s Harry Maguire.