The '30 Rock' star and his yoga instructor wife of eight months said her pregnancy came as "a wonderful surprise" and they feel very "lucky".
Hilaria, 28, confirmed the news on Tuesday on 'Extra', for which she acts as a part-time correspondent, saying: "We've having a baby. (It) was a surprise, a wonderful surprise."
Alec, 54, who already has a 17-year-old daughter Ireland with ex-wife Kim Basinger, revealed he was unaware that his wife was even taking a pregnancy test at their country home and was amazed to discover the news when he heard her screaming in the bathroom.
He said: "There's a scream I heard, which is a scream normally reserved [for] if there's a spider in the house. It really is the most amazing thing. I'm lucky."
Hilaria has already noticed a change in her body and she can't wait to start preparing their home for the new arrival.
She said: "I'm showing. This is actually gonna happen, now we can start the nursery, the everything, the dreaming!"
Alec previously revealed that he hoped to become a stay at home father if Hilaria ever got pregnant.
He said: "I keep telling my future wife that I want her to get rich because I want to retire. She teaches yoga. I want her to become the world's first billionaire yoga teacher. I know it is a long shot, but that's the plan I'm sticking with right now. I want to have a baby and stay home and make the pancakes before I send my wife out to work every day to pay the bills."
The couple were recently forced to deny rumours they were having a baby because they weren't ready to announce the news.
Hilaria first sparked speculation she was expecting late last month when she showed off what looked like a baby bump while filming a segment for 'Extra' that saw her pull off some impromptu dance moves.