They announced their happy news today on Twitter and revealed that they have named him Elijah Joseph.
The happy couple celebrated their first wedding anniversary the day after his birth.
Michael, 36, took to his Twitter page first to make the announcement: "Hey everyone, sorry for the lack of contact and being off the radar 4 a few days. Hope you guys had a great festive time.
"We have news... @angellicabell and I would like to announce the birth of our beautiful baby son, Elijah Joseph, who arrived on Boxing Day. He is adorable!'
"We also celebrated our 1st WEDDING ANNIVERSARY yesterday, so it's been an exciting and eventful few days.
"THANK U to our twitfam who have supported us over the last 9 months and for ur tweets of concern over the last few days - they meant a lot.'
He later added: "At the moment, I'm just basking in dirty nappies!"
Their pages were soon flooded with well-wishers passing on their congratulations including tweets from their celebrity friends.
Sports presenter Gabby Logan was one of the first and she wrote: '@MikeyUnderwood congratulations and give our love to Angelica and Elijah, love Gabby and Kenny x.'
Michael replied to the couple, who have six-year-old twins Reuben and Lois, and said: 'Thank you so much Gabby! We should all meet up in the new year, so @angellicabell and I can get some baby advice. :).'
Angellica, 34, and Michael, who worked together on CBBC, married in New York in December 2010. Angellica had previously admitted her pregnancy was a 'whoopsie moment' accident, although they were both looking forward to the birth.