Presenter Bell gave birth to son Elijah Joseph Underwood on December 26.
She tweeted: "[We] would like to announce the birth of our beautiful baby boy, Elijah Joseph, who arrived on Boxing Day. He is adorable!"
The pair met in 2000 while presenting CBBC together, and were married in December last year.
She added: "We also celebrated our 1ST WEDDING ANNIVERSARY yesterday so it's been an exciting and eventful few days."(sic)
Angellica Bell took part in reality series 71 Degrees North earlier this year.