Luciana, 34, is due in the fall. "Everybody's really happy," a rep for Damon, 39, tells PEOPLE.
The couple already have three daughters: Alexia, 11, who is Luciana's child from a previous marriage, Isabella, who will be 4 in June, and Gia, 20 months.
Damon is a "phenomenal" father, his close friend George Clooney told PEOPLE in 2007. "He absolutely adores those kids. He's doing it really well."
Damon and his wife were married in 2005. After Isabella was born, PEOPLE's 2007 Sexiest Man Alive told a British newspaper that having a family had transformed his life.
"I really used to have no life outside movies. I'd work all day, go to the gym and go to sleep," he said. But once Isabella arrived, "that was it for me and working out because I wanted to get home to see my daughter before she went to sleep."
Leave your best wishes for the Damons at PEOPLE Moms & Babies!
With reporting by JULIE JORDAN