Giannini was born La Spezia, Liguria, Italy. He studied at the Accademia Nazionale in Rome, and made his film debut in a small part in Fango sulla metropoli in 1965. He appeared in supporting roles in Anzio and The Secret of Santa Vittoria, and starred in the original version of Swept Away. In 1971, he appeared in E le stelle stanno a guardare, a television adaptation of A. J. Cronin's novel, "The Stars Look Down".
In 1976, he starred in Seven Beauties, for which he was nominated for the Academy Award for Best Actor, which is unusual in that his performance was given entirely in Italian. He dubbed Jack Nicholson's voice in the Italian release of both The Shining and Batman; and is the official Italian dubber of Al Pacino. His fluency in English has brought him a number of featured roles in Hollywood productions, most notably as Inspector Pazzi in Hannibal. He has also appeared in A Walk in the Clouds as the protective father, Alberto Aragón, and as Padishah Emperor Shaddam IV in the 2000 Dune miniseries.