England left-back Shaw became the most expensive teenager in history when he moved from Southampton to Manchester United for £27million this summer.
Irwin had a 12-year stretch as United's undisputed first-choice left-back, and he believes Shaw, who only turned 19 a week ago, has the potential to hold on to the same position for a similar length of time.
"He is going to be a fantastic signing for years to come," said Irwin, who played 529 times for United.
"He showed he has great pace for England at the World Cup and in the warm-up games.
"He has always been great going forward, we have seen that in the Premier League.
"There was talk of Chelsea being in for him so I am delighted that he signed for United.
"He is a fantastic player, who will improve and get stronger."
Irwin believes the hefty transfer fee United paid for Shaw will not prove to be a burden for him even though he only made his full Premier League debut 16 months ago.
"As a young lad, you don't feel the pressure as much as older players," the Irishman added.
"Market forces dictate what you have to pay for players. But he has been playing in the Premier League for the last two years with Southampton.
"He is a strong lad for a 19-year-old. He has great pace, great going forward.
"He is still only young. He will make mistakes defensively. We have to accept that, but he is a fantastic player."
Irwin has also predicted that new manager Louis van Gaal will be a resounding success at Old Trafford.
"Slowly but surely he will be able to put his own imprint on the way he wants Manchester United to play,” he said.
"The manager has won trophies all over the world. His experience will be good for us. Next season we have to aim for the summit."