Bonucci joined the Rossoneri from the Serie A title-holders this month for a reported fee of €40 million, announcing Milan as a force to be reckoned with in the transfer market following a takeover by Chinese investors.
Despite suggestions of a rift with Juve coach Massimiliano Allegri, few expected the Azzurri centre-back, a key man for club and country, to leave Turin.
Montella, though, having received a tip-off, ensured his team did not miss an opportunity to stage a major coup.
"I was convinced it was achievable, I trusted those who told me, while my leaders had a different perception," he was quoted as saying by 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'."
Montella is not concerned about Bonucci disrupting the dynamic among the squad and acknowledged his arrival may prompt a change to a three-man defence in 2017-18.
"It intrigues me as an idea," he said of the potential for a switch in formation.
"But I must say that with these players we can really use so many systems.
"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."
Having spent big to overhaul the team, Milan are expected to allow several players to depart before the transfer window closes next month.
Among those seemingly at risk of being offloaded is M'Baye Niang, but Montella indicated the French forward could yet earn a reprieve.
"Niang against Bayern made a brilliant match," he said of Milan's 4-0 International Champions Cup victory over the Bundesliga title holders.
"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."