The actor and wife Brady Cunningham welcomed a daughter, Marlowe Rivers Schwartzman, on Saturday, Dec. 4 in Los Angeles, his rep confirms to PEOPLE exclusively.
"I'm lucky I found a woman that I love and that's amazing," Schwartzman, 30, who stars in the HBO hit Bored to Death, said last fall.
"I'm having a family and I feel very happy. I try to be a good father-to-be. I try to treat my wife well [so she can] enjoy these months.”
Schwartzman and Cunningham, a fashion designer, wed in July 2009.
Reporting by OLIVER JONES