The Agnelli name has been absent from Juve's boardroom since Gianni's death in 2003 and Italy's best supported club have suffered scandal and disappointing results ever since.
"Andrea is not only a representative of our family but a person that loves Juventus in a genuine way," John Elkann, grandson of Gianni and president of the holding company which controls FIAT and Juve, told the website.
The 34-year-old Agnelli takes up the post at the end of the season with Jean Claude Blanc reverting to his position as chief executive.
The president's role is limited but Juve fans, who have had to deal with a match-fixing demotion in 2006 and a poor campaign this term, will be glad of a link to a glorious past which included two European Cups under Gianni's rule.
Other changes are expected at Juve, who are sixth in Serie A, but the club have refused to confirm or deny interest in Liverpool coach Rafael Benitez after fevered media speculation.
Alberto Zaccheroni, who took over from the sacked Ciro Ferrara in January, has not improved the side's form and there has been no sign his contract will be extended beyond June.
Media reports have also said former midfielder Pavel Nedved, who retired at the end of last season and has been sorely missed on the field, will soon be appointed as youth team coach.
Highly-regarded Sampdoria sporting director Beppe Marotta has also been linked with Juve as the club try to move on.
However, reminders of their demotion are never far away.
On Wednesday the Italian soccer federation announced after a review that the 2006 ban on former Juve general manager Luciano Moggi, the chief accused in the matchfixing scandal, still applied to all roles in Italian football.
Moggi is facing a criminal trial over the affair.
