Giannini was born in La Spezia, Liguria, Italy. He studied at the Accademia Nazionale d'Arte Drammatica in Rome, and made his film debut in a small part in I criminali della 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 1967, he was a special guest on an episode of Mina's TV show "Sabato Sera". In 1971, he appeared in E le stelle stanno a guardare, a television adaptation of A. J. Cronin's novel, The Stars Look Down.