The 35-year-old actor and Smith welcomed the baby girl on Sunday, reported Us magazine.
Bartha and the personal fitness trainer got engaged in May 2013, and tied the knot back in January in Oahu, Hawaii.
During their intimate ceremony, the newylweds were feted by Reese Witherspoon, her husband Jim Toth (who is also Bartha's agent), Jesse Eisenberg, and his 'Hangover' costar Ken Jeong.
Bartha has earlier dated Ashley Olsen from 2009 to 2011.