Born in Bacoli, Province of Naples, Salemme began his career in 1976, with the stage company of Tato Russo.

[1] The following year he joined the theatre crew of Eduardo De Filippo, later led by his son Luca, where he worked until 1992.

[2] In the 1990s, Salemme started writing and producing his own comedy plays, enjoying a large success with E fuori nevica.

[1][3] He debuted in the movie industry the early 1980s as a character actor; following his increasing popularity on stage, in 1998 he wrote, directed and starred in the comedy film L'amico del cuore, which enjoyed a considerable commercial success.

[1][3] In the following years, Salemme alternated his personal projects, on stage and on the big screen, and leading roles in films by other directors, usually comedies.