Agnelli died, aged 81, after losing his fight against prostate cancer.
He was also honourary president at Juventus and kept in daily contact with the team heading up the Formula One team.
Said UEFA chief executive Gerhard Aigner: “I am very saddened to hear of the death of Giovanni Agnelli, the man also known as ‘L’Avvocato' [The Lawyer]. He was a man who was passionate about sport and in particular football.
“Thanks to him Juventus FC has become one of the greatest clubs in Europe with a fantastic tradition - together they have written many famous chapters in European football. He will be sorely missed.”
Edoardo Agnelli, father of Gianni and the son of Giovanni, the founder of Fiat, took charge of Juventus in 1923. Edoardo presided over a period of unprecedented success at the Turin club, Juventus winning five successive championships between 1931 and 1935, before he was killed in a plane crash in Genoa on 14 July 1935.
Yet the Agnelli family name lived on, Gianni taking control of the club in 1947. Gianni had a similar impact to his father, Juventus winning their eighth and ninth Scudettos in 1950 and 1952.
Gianni stepped down in 1953, three years before his brother, Umberto, was elected president, the third Agnelli to hold the esteemed position.
A Juventus supporter since the age of five, Agnelli remained a passionate follower of the club and frequently attended training at the Stadio Comunale, the club's former stadium and current training ground. Agnelli was appointed an Italian senator for life in 1991, five years before he relinquished the presidency of Fiat to become the company's honorary president.
Ferrari team boss Jean Todt added: "Ferrari was always a special company for him and its achievements were of particular significance to him.
"He was always very interested in what went on at Maranello and supportive of our efforts over the years it took to become successful once again and he was involved in all our decisions.
"When, finally, we managed to win again, he shared our feelings of relief and joy. We knew we could always count on his presence and support. His passing marks the end of an era."
