Agostini was born in Trieste, Italy. After early training with his grandfather, he studied violin at his hometown's conservatory of music, in Trieste, then in Venice, and later at the Accademia Chigiana in Siena.
Před zahájením herecké kariéry pracoval jako policista v Římě a studoval herectví na Centro Sperimentale di Cinematografia a u Silvia D'Amica na Accademia Nazionale di Arte Drammatica.