"Mom and baby are fine and everyone is very happy," Astin's rep, David Lust, tells PEOPLE.
Astin, 34, and Christine, 37, both UCLA grads, wed in 1992.
Astin is best known for his role as the hobbit Samwise Gangee in the Lord of the Rings trilogy. He is about to begin production on Adam Sandler's new comedy, Click, in which he will play opposite Kate Beckinsale.
Astin, whose parents are actors Patty Duke and John Astin (Gomez on the 1960s TV series The Addams Family), told PEOPLE in 2002 that being a good husband and father are his most important roles: "My priorities are clear. I provide for and protect my family."