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Rubini started to play basketball for his high school team in his native Trieste, where he graduated in 1941. The same year he began to play for Olimpia Milano, the most prestigious Italian League basketball club at that time. He however had a long-lived passion for water polo: this led him later to become one of the rare world sportsmen to play at the highest level in two different team sports.
In 1946, he won a silver medal with the Italian national basketball team at the EuroBasket 1946, held in Geneva. The following year, he also won a silver medal at the European Championships, but this time with the Italian national water polo team. In the meantime he had assumed the role of player-coach of Olimpia Milano: in 1948, however, he was called by the national teams of both sports. Rubini chose water polo, and won a gold medal at the 1948 Summer Olympic Games in London, beating the Netherlands in the final. With Rubini as a full-time player, Italy could boast what was to be called the "Golden Settebello", one of the most valuable water polo teams ever, which also won a bronze medal at the 1952 Summer Olympics and at the TurinEuropean Championship of 1954. In both the events, Italy was behind traditional rivals of Yugoslavia and Hungary.
Rubini, also as player-coach, won 6 national titles in water polo with Canottieri Olona of Milan, Rari Nantes of Naples and Camogli teams. He totaled 84 caps for the Italian national team, 42 of which were as a captain.
As a basketball player, Rubini won 5 national titles in a row, from 1950 to 1954. After 1956, he devoted only to the coach role, winning 10 national titles with Olimpia. In these years, he set an unparalleled record of 322 victories and 28 defeats. As coach of the Milan team, Rubini totaled 488 victories, including the European Champions Cup (Euroleague) in 1966, and two European Winner's Cups in 1971 and 1972: these were the first international victories of Italian basketball clubs.
As the manager of the Italian national basketball team, Rubini took also part in the first international victories of Italy: these include the silver medal at the 1980 Summer Olympic Games. At the EuroBasket, Italy was first in 1983 at Nantes, second in 1991 at Rome, and third in 1985 at Stuttgart.
Rubini was involved with his beloved sports until his death: he promoted water polo formation for young athletes, and was Honorary President of Olimpia Milano.