Gimondi had been on holiday with family and friends when the incident happened. Longtime friend Domenico Fichera said all efforts to resuscitate Gimondi were made but failed.
"He died in my arms," Fichera said. "When we recovered him by the sea, in front of the private beach of the RG Naxos Hotel, he had little pulse.
"Later, despite the desperate attempts at resuscitation, cardiac massage, and mouth-to-mouth breathing by the lifeguard and paramedics, who arrived at the scene swiftly, we had to note the death."
Gimondi won the 1965 Tour de France in his first season as a professional, aged 22.
He won the Giro d’Italia two years later and the Vuelta a Espana in 1968.
Gimondi also won the Giro in 1969 and 1976 to take his Grand Tours tally to five. He retired in 1978.
“A great champion who made our sport more human has left us, a great man,” the Italian cycling federation said in a statement.
Jacques Anquetil, Eddy Merckx, Bernard Hinault, Alberto Contador, Vincenzo Nibali and Chris Froome are the other six riders to have won all three Grand Tours.
Five-time Tour de France winner Merckx told Italian news agency ANSA, "A man like Gimondi is not born every day. With him goes a piece of my life. He was among the greatest ever."

Jacques Anquetil (L) with Eddy Merckx (C) and Felice Gimondi in 1970. (Getty) Source: Getty