The Premier League champions have been long-term admirers of the centre-back, and he will move to Manchester this week before signing a four-year deal with United on his 16th birthday on October 19.
Chelsea and Aston Villa have both also been tracking the talented teenager, who plays for Rock Celtic - a team based in Blackrock just outside Dundalk.
Despite the interest from Chelsea and Villa, the report claims United were always in pole position to seal the signing after Dunne joined their Belfast-based academy aged 10.
And the 6-ft-2-in centre-back can't wait to start training as an official Manchester United player.
"There were other teams interested but from the minute I went to Carrington, I knew that was the right move for me," Dunne told the Irish Independent.
"It's a huge club with a great history and they have been very supportive of me right from the start.
"I know it will be a massive challenge but I will be surrounded by good players and excellent coaches and that can only help improve my game. I can't wait to get started."
The report claims Dunne has visited several Premier League clubs over the last 12 months, but while the likes of Chelsea and Villa showed strong interest, United were always the dream destination for the 15-year-old.
The Premier League champions also relied on the persuasion skills of United legend Brain McClair, who held talks with the Dunne family over a move to Old Trafford.
Dunne led Dundalk schoolboys at Northern Ireland's Milk Cup, where Premier League scouts converge to watch the best young players in that age group.