"We're so thrilled and we can't wait to meet our baby," the couple told People.com in a statement Tuesday.
Hilaria expects to deliver the child this summer.
Baldwin, 54, married the 29-year-old yoga instructor in June 2012, following a three-month engagement.
The baby will be his second child. He also has a 17-year-old daughter from his previous marriage to actress Kim Basinger.
Baldwin, who recently wrapped up a seven-season stint on the TV sitcom "30 Rock," will headline the first Broadway production of a Lyle Kessler play, "Orphans," starting March 19.