Brazzi had an extensive filmography, much of it in Italian and French films, but the film that propelled him to international fame was Three Coins in the Fountain (1954), a Hollywood blockbuster, followed by the leading male role in David Lean's romance Summertime (1955). Other Brazzi's notable roles include an early Hollywood part in Little Women (1948), as well as visible roles in The Story of Esther Costello (1957), South Pacific (1958), The Barefoot Contessa, The Light in the Piazza (1962), and as the murdered Roger Beckermann in The Italian Job. In 1966, he starred in the family feature, The Christmas That Almost Wasn't.
In 1940, Brazzi married Lidia baroness Bertolini (1921-1981), to whom he stayed married until her death. The couple had no children. In 1982, he married the German Ilse Fischer. There were no children from the marriage. Brazzi died in Rome on Christmas Eve 1994 at the age of 78, from a neural virus.