The couple, already raising three children, welcomed a girl, Stella Zavala Damon, who was born on Wednesday in New York.
"Mom and baby are both healthy," Damon's rep tells PEOPLE. "The whole family is thrilled."
Damon, who turned 40 earlier this month, and Luciana, 35, wed in 2005 and have two children together – Isabella, 4, and Gia, 2. Luciana also has a daughter, Alexia, from a previous marriage.
Damon currently stars in Hereafter, which opened wide on Friday.