The actor and wife Zoe Buckman, who wed in June in a private ceremony, will be first-time parents, his rep confirms to PEOPLE, who adds that the two "couldn't be more thrilled."
Buckman, a photographer, and Schwimmer, 44, met in London in 2007, and announced their engagement in March 2010.
Speaking to PEOPLE in 2006 about his desire to start a family, the former Friends star said he was eager to be a dad – in due time.
"I think it's gonna have to wait until I settle down and have a family," he said at the time. "It will happen when it feels right. Maybe part of me is waiting for myself to slow down a little and be ready to stay put. I'm confident it's gonna happen."