Crozza was born in Genoa. He attended an acting school in the same city, where he graduated in 1980.
He has worked for many years with the Gialappa's Band trio on Mediaset and in the Sunday show Quelli che... il Calcio on Rai. Crozza has also starred in a number of films, including the 1995 movie Peggio di così si muore by Marcello Cesena. Over his career, he has received both praise and criticism from Italian commentators: he was notably criticised over his satire on Pope Benedict XVI in 2006 and about Silvio Berlusconi at the 2013 Sanremo Music Festival.
- Peggio di così si muore on IMDb
- ""Basta satira sul Benedetto XVI" - Insorge il segretario del Papa". La Repubblica. 14 November 2006. Retrieved 13 February 2013.
- "Canzoni e satira, parte il Festival "politico" - Crozza fischiato mentre imita Berlusconi". Corriere della Sera. 13 February 2013. Retrieved 13 February 2013.