Felice Gimonde, one of seven winners of the three major cycling events, died at the age of 76 after suffering a heart attack while swimming on Sicily on Friday.
"The great hero who made our game more human is gone, a great man," the Italian Cycling Federation said in a statement.
He won the Tour de France in 1965 in his first professional season at the age of 22.
He won the Italian Grand Prix two years later and Spain in 1968. Gimonde also won the Italian Grand Prix in 1969 and 1976, taking his tally to five races before retiring in 1978.