Coppola is the daughter of filmmaker Francis Ford Coppola. Her film credits include "Somewhere," "Lost in Translation," "Marie Antoinette" and "The Virgin Suicides." She married director Spike Jonze in 1999 and they divorced in 2003.
Mars is the lead singer of the band Phoenix.
The couple are the parents of 4-year-old Romy and 1-year-old Cosima.
Their wedding ceremony is expected to take place in August at her family's villa in Italy.
"Yes, they are getting married and having an intimate family wedding," her representative told People.com.