Milan's hardcore supporters, known as Ultras, were among those who had wanted the phlegmatic coach to keep his job after leading a young and rebuilt Milan team to third place in Serie A this season.
"The relationship with the coach, which has never been interrupted, continues with confidence and in absolute and mutual respect," Berlusconi said in a statement on Milan's website.
"We had a cordial and frank discussion with Galliani and Allegri in which we looked over and analysed last season and clarified a few things," said former Italy Prime Minister Berlusconi.
"We reached an agreement over the rights and obligations of the club to the coach and of the coach to the club. We also talked about the type of game that Milan will have to play next season and drew up the guidelines for the transfer market."
Ten days ago, Milan's Curva Sud supporters group issued a statement praising Allegri and criticising the idea of replacing him.
