Van Persie is expected to make the switch from Arsenal to United in the next 24 hours after the two clubs agreed a fee, reported to be £24 million. for the 29-year-old.
Carrick heard the news after making his England comeback in the friendly international with Italy, and said: "If it goes through then it's great news. We welcome him, he had a terrific season last year. He'll just strengthen our squad even more."
When United won the treble in 1999 they had Andy Cole, Dwight Yorke, Ole Gunnar Solskjaer and Teddy Sheringham in attack.
Comparisons are likely to be drawn with the new crop, which in addition to Van Persie will include Wayne Rooney, Javier Hernandez and Danny Welbeck.
Carrick added: "The manager has gone on record as saying that the team in '99, because of the four forwards they had, was one of the most exciting and one of his happiest times. So hopefully we can repeat something like that.
"It's a huge boost. He's a terrific world class player and it's great to bring in players of that ability and give everyone a boost."
Arsenal now need to find a new captain for the fourth time in seven years and Belgian defender Thomas Vermaelen is believed to be among the favourites to assume the armband in time for Saturday's game against Sunderland.
The defender has admitted he was disappointed to hear of Van Persie's imminent exit.
"I am disappointed because I wanted him to stay at the club," he told Sky Sports News.
"He was fantastic for us in the last year, scored lots of goals and I am disappointed he is going, but we have to focus on the next season with Arsenal. We have to fight and I am confident we have a squad to win something."
Arsene Wenger said Arsenal had already brought in replacements for Van Persie and said selling Van Persie was unavoidable.
"He is at Manchester United, unfortunately for us. The transfer was finalised in the afternoon," said Wenger whilst working for French TV station TF1. "It's never great to lose players of that quality but he only had a year contract so we do not have a choice."
He went on: "We have already recruited since we bought (Olivier) Giroud and (Lukas) Podolski who originally were intended to offset the departure of van Persie."