Born in La Spezia, Italy, Giannini studied at the Academia Nazionale in Rome, and made his film debut in a small part in Fango sulla metropolis 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 1976, he starred in Seven Beauties, for which he was nominated for the Academy Award for Best Actor. He dubbed Jack Nicholson's voice in the Italian version of The Shining, for which Nicholson sent him congratulations. He also starred in Hannibal.