The Red Devils announced on the final day of the summer transfer window that they had a deal for the 18-year-old in place.
He will not join their ranks until January, but an agreement that could end up being worth up to £37 million ($48m) has been pushed through.
United believe they are acquiring one of the hottest prospects in European football, with Diallo’s potential having registered on their radar for some time.
He first came to their attention when facing arch-rivals Manchester City in the UEFA Youth League, with efforts made from that point in 2019 to bring him onto their books.
Percassi told L’Eco di Bergamo of how a protracted saga unfolded: “The negotiation with Manchester United lasted almost a year.
“The details and scenarios are crazy. Meeting after meeting we learned unimaginable things.
“This leads to the growth of the club and enriches the work of everyone, from the general manager, Umberto Marino, to the entire staff.”
Percassi added: “A few days after the Youth League game against Manchester City, the other Manchester contacted us.
“They had followed him, the real negotiation started. We went twice to England. The text of the final agreement is a contractual masterpiece.
“The professionals involved in the operation are of a high level. In terms of negotiations, we have learned a lot.
“And it is above all thanks to Luca’s (Percassi, Atalanta CEO) work that we arrived at the final figures. It was an operation we couldn't refuse.
“If the boy becomes great, we will have recognition for a long time. If he's not lucky, we're protected.”
The man who first spotted Diallo’s talent, Giovanni Galli, revealed after a deal with United had been announced that a transfer had been in the pipeline for some time.
He told Football Italia: “I know a scout of Manchester United very well as we usually meet at games. He used to tell me that the club sent him several times to watch the player.”
Galli added on a hefty asking price: “It is high, but there is a reason behind it.
“Traore still needs to get a work permit since he has not played with his national team yet. The club need to have valid reasons to take him to the UK.
“One reason is that the player is coming from a top team and with Atalanta that have been playing international competitions over the last few years, there are no problems to prove it.
“The second reason is the price tag. A €40m signing means he is an important investment for the club.
“If the cost would be €1 or 2m it may have been more difficult to get the work permit. That being said, €40m is still a lot of money.”