The legendary former Old Trafford left back has tipped the 37.5 million euro summer signing for success after he opted 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 euro
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 preseason tour of the USA. "He is going to be a fantastic signing for years to come."
Because of the player's potential, Irwin is unfazed by the fee United paid to land Shaw amid interest from Chelsea.
"Market forces dictate what you have to pay for players, and there was talk of Chelsea being in for him," he said. "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."