Shaw became the most expensive teenager in history when he moved from Southampton to Manchester United for £27m this summer.
Irwin, who had a 12-year stretch as United's undisputed first-choice left-back, believes 19-year-old Shaw has the potential to hold on to the position for as long as he did.
"He is going to be a fantastic signing for years to come," Irwin is quoted as saying by Sky Sports. "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."