Milan have been busy overhauling their squad but Vincenzo Montella's men stunned the world when they managed to sign Serie A-winning defender Bonucci for €42 million last month.
Mirabelli admitted Milan – bankrolled by new Chinese owners – did not plan to sign the 30-year-old centre-back.
"Bonucci's transfer wasn't planned, but it was an opportunity we had to grab as it went past," he Rai Sport.
"I was talking to [agent Alessandr] Lucci about other players and he kept making jokes about Bonucci. Over the first few days, I didn't even tell [CEO Marco] Fassone.
"Then I saw the lad really did want to come to Milan and we worked out the negotiations very quickly."
After years of mediocrity, Milan have invested heavily in 2017-18, signing Bonucci, Andre Silva, Lucas Biglia, Hakan Calhanoglu, Andrea Conti, Mateo Musacchio, Ricardo Rodriguez, Franck Kessie and Fabio Borini.
Milan could still add to their squad before the transfer window shuts, with Pierre-Emerick Aubameyang, Andrea Belotti, Nikola Kalinic and former striker Zlatan Ibrahimovic all linked to San Siro.
Asked about the possible return of Ibrahimovic or Aubameyang, Mirabelli said: "We'll look at what is out there and you never know in life.
"A few old faces may well return, but I do not intend to allude to Ibrahimovic. We're keeping our feet on the ground and evaluating the situation."