His death was announced by Inter on the day the club marked 10 years since its Serie A, UEFA Champions League and Coppa Italia treble.
Simoni had a well-travelled coaching career and guided seven teams to promotions from Serie B to the Italian top flight, a record.
He suffered a stroke last June from which he never fully recovered and was taken to hospital when his health began to deteriorate shortly before his death, newspaper La Gazzetta dello Sport reported.
Simoni coached clubs including Lazio, Napoli, Torino, Brescia and Cremonese, but arguably his finest hour came with Inter when the Nerazzurri thumped Lazio 3-0 at Parc des Princes on 6 May, 1998, to secure the European trophy.
Inter issued a statement on Saturday (AEST), which read: "Today, 22 May, he left us. Not just any date, the most Inter-related date of all.
"We remember Gigi Simoni and will miss everything about him. First and foremost, his gentlemanly way of being. His way of living, both in life and football, was never over the top. His football reflected that: it was humble, functional and capable of making the most of what he had on offer."
Goals from Ivan Zamorano, Javier Zanetti and Ronaldo gave Inter its third UEFA Cup success of the 1990s.
It came in Ronaldo's first season at the club after his move from Barcelona, before the Brazilian would encounter the injuries that blighted his San Siro stay.
Simoni's Inter almost won the Serie A title that season too, eventually finishing in second place, five points behind champion Juventus.
The experienced coach was awarded the Panchina d'Oro — Golden Bench — for his achievements in that 1997-1998 campaign, but lost his job before Christmas in the next season.
Lazio and Napoli were among the clubs that offered condolences to Simoni's family, on the news of his death.
Cremonese, whom he led into Serie A and also to an Anglo-Italian Cup triumph over Derby County at Wembley in 1993, paid a fond tribute.
They reflected on his achievements in a four-year stay, which saw him voted the club's coach of the century, stating: "Travel well Gigi, we will miss you but you will remain forever in the history of the Cremonese and in the hearts of all the Grigiorossi fans."
Inter's statement on its official website concluded: "The world of football has lost a great coach and a wonderful person.
"This is how we remember him: with his white hair, in our dugout, while he enjoyed the magic of Ronaldo with a smile on his face, enveloped by the fans' affection. Farewell Gigi, we'll miss you."