Sharing a sweet picture of the newborn's hand on his Instagram account, Dec wrote: "Shortly before 10am yesterday, 23.7.2022, Ali and I welcomed the arrival of our son, Jack Anthony Alphonsus, a very welcome ray of light.
"He is wonderful and Isla is beyond excited to be a big sister! D x"
It's thought the child's middle names are in honour of Dec's friend and long-term presenting partner Ant McPartlin, plus his father Alphonsus Donnelly, who passed in 2011.
Dec has been married to his wife Ali since 2015, though the pair knew each other for almost 20 years as she worked as his manager.
They welcomed their daughter Isla in 2018 and writing in Ant & Dec's joint book Once Upon a Tyne, Dec spoke about what it was like becoming a father.
"Becoming a dad has completely transformed me. At first, like all expectant parents, I didn't truly understand how much it was going to change me," he wrote.
"I just thought it was another little person coming to live in the house. It opened up a whole other side to me, a side I didn't know existed.
"I felt a love that I didn't realise it was possible to feel. Everything I do, every day, is for my daughter now."
The joyful news comes just two weeks after Dec's older brother, Father Dermott Donnelly, died at the age of 55.
Father Dermott, who had worked as a Catholic priest for the past 30 years, passed away after a short illness, with Dec giving a statement via social media.
"I am heartbroken to tell you that my darling brother Fr Dermott, @TweeterPriest, sadly passed away this afternoon," he wrote.
"We are all beyond devastated. Thank you for your messages of sympathy and support, they are appreciated."
Ant & Dec are expected to return to screens later this year to host a new series of I'm a Celebrity. Ant recently shared the news that the show is due to return to Australia, after two years at Gwrych Castle in Wales.
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