Pier Silvio Berlusconi, 46, will replace Giuliano Adreani, the company said in a statement after a board meeting.
The younger Berlusconi was also confirmed as the media group's deputy chairman, a position he has held since 2000.
Pier Silvio Berlusconi is also a director of Fininvest, the holding company controlled by the Berlusconi family.
The announcement that Pier Silvio will be taking over the reins at Mediaset comes amid speculation that French media group Vivendi is eyeing the Italian company.
A report in French weekly La Lettre de l'Expansion this week said Vivendi was "actively looking at" acquiring Mediaset assets.
It also said 78-year-old Silvio Berlusconi, currently in the process of selling his stake in AC Milan football club, was considering refocusing on books and the press through his Mondadori publishing company.