AC Milan coach
"I was convinced it was achievable, I trusted who told me, while my leaders had a different perception," told Gazzetta dello Sport.
"I sent [sporting director Massimo] Mirabelli at least 10 messages a day, with only three words: 'Good morning, or good night, director: Bonucci'."
Bonucci's arrival has brought with it speculation that Montella may opt to switch to a back three, and the Italian coach has not dismissed the prospect.
"It intrigues me as an idea," he said.
"Bonucci is a highly competitive professional, he will be an example for young players. I do not know if without him Juve has been weakened, but we certainly have strengthened ourselves.
"[And] I do not think he will be too big of a presence in the locker room."
Milan are expected to sell players after their influx of high profile signings, and one player believed to be at risk of an exit is young striker
"Niang against Bayern made a brilliant match," he added of Milan's 4-0 International Champions Cup victory over the Bundesliga champions.
"He can become a top player, but he needs to improve himself in managing himself when things are fine. There is no reason not to believe in him, it depends more on M'Baye."