The inventor, who triumphed in series seven of the British reality show to win investment from Lord Alan Sugar, shared the news with his followers on Twitter.
Pellereau wrote: "AMAZING NEWS - My wife Sarah & I are expect a baby. Just had 20wk scan. #BabyInventor on the way. (sic)"
The 33-year-old received messages of congratulations from fans and was told to "sleep like you've never slept before" in preparation for the baby's arrival.
One follower tweeted: "Congrats - always reassuring when an inventor can work out the simpler things in life without over-engineering them!"
Pellereau beat runner-up Helen Milligan in the 2011 series of The Apprentice. Since winning the show, he has launched the Stylfile range, based on his S-shaped nail file design.