The couple married in a beautiful villa owned by Coppola's father, famed director Francis Ford Coppola, in the tiny town of Bernalda.
She wore a lavendar dress designed by Azzedine Alaia.
The couple have two children: Romy, 4 1/2, and Cosima, 15 months old.
Coppola is best know for "Lost in Translation" for which she wrote the screenplay and also directed.
It's a second marriage for Coppola, who was married to director Spike Jonze from 1999 to 2003.
The wedding, attended by 80 guests, was a stark contrast to last week's celebrity nuptials: the extravagant wedding of Kim Kardashian and Kris Humphries.