The legendary former Old Trafford left-back has tipped the €37.5 million summer signing for success after opting to join Louis van Gaal's side despite interest from Chelsea
Shaw, who was part of the England World Cup squad this summer and started the final group game against Costa Rica, has moved to United from Southampton for €37.5 million.
And Irwin is expecting big things from the teenage left-back, who only turned 19 earlier in July.
"He has pace, is great going forward and is still only young," Irwin told reporters in Los Angeles during the club's pre-season tour of the USA.
"He is going to be a fantastic signing for years to come."
Irwin is unfazed by the €37.5m United paid to land Shaw amid interest from Chelsea due to the player's potential.
He said: "Market forces dictate what you have to pay for players and there was talk of Chelsea being in for him.
"We have to accept he will make mistakes defensively. But he has been playing in the Premier League for the last two years with Southampton and he is only going to get better."