The initial £27million down payment, which eclipsed the B£25.8million fee United paid for Wayne Rooney, raised a few eyebrows as Shaw only turned 19 a week ago.
But Irwin is sure United have made a sound investment in the teenager, who went to the World Cup ahead of 107-cap defender Ashley Cole, who subsequently retired from international football.
Irwin had a 12-year stretch as United's undisputed first-choice left-back, and he believes Shaw 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 the former United defender, who played 529 times for the club.
"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."
Although he supported Chelsea growing up, Shaw chose United ahead of the London club.
United are so confident about Shaw's ability to succeed that they are willing to let experienced campaigner Patrice Evra depart even though he signed a new contract in May.
Back-up Alexander Buttner has also been sold to Dynamo Moscow.
Irwin is sure the hefty transfer fee United paid for Shaw will not prove to be a burden for the young left-back 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," Irwin 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 also believes new manager Louis van Gaal will be a resounding success at United.
Van Gaal's first game in charge comes on Wednesday when United take on the Los Angeles Galaxy in the first game of their US tour.
Because Holland reached the semi-finals of the World Cup, Van Gaal only has a month to get to know his squad before the season starts, but Irwin is sure the 62-year-old will be able to turn United into title contenders after a fallow year under David Moyes.
"We would have liked him in earlier, but he did well with the Netherlands," the Irishman said.
"Slowly but surely he will be able to put his own imprint on the way he wants Manchester United to play.
"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."
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