The forward signed last week after Crystal Palace accepted a £10million bid from the club.
And Gayle can't wait to play for United manager Benitez.
"It's a massive thing for me to be playing under a manager like that," said the 25-year-old
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"For him to ask me to come to the club is a dream come true.
"He's been a legend in the Premier League and abroad as well. Playing under him is going to be a dream come true."
Gayle also revealed that ex-Newcastle winger Andros Townsend had recommended a move to the club.
Townsend joined Palace last week after deciding he wanted to stay in the Premier League.