Caterina shared the happy news with her Twitter followers by posting an adorable photo of her newborn son's feet.
"It's official at 9 30am today I became a Daddy," JJ wrote within an hour of the birth. "The healthy little boy has arrived at a weight of 6lb!!!!! soooo happy right now :)))) xx".
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The proud parents named him Princeton J Alexander.
The X Factor star kept his fans up to date with the progress of Caterina's labour.
"AND NOW WE WAIT!!! :-))))))) x," he wrote to his 241,417 followers on Wednesday evening.
Excitement built throughout the night and he took to the social media site writing, "NOT LONG NOW!!!!!! Sooooooo excited :))))) xxx"
Congratulatory messages came flooding in for the couple.
One Direction's Niall Horan wrote, "Congrats JJ mate!".
JJ's bandmates were also quick to tweet their excitement.
"SOOO HAPPY for JJ and Cat!!," Josh wrote. "It's an amazing day and couldn't happen to 2 more amazing people. Chuffed to bits. The baby is gonna be beautiful.
George tweeted, "Congratulations JJ and Cat! New little one in the family now so proud of you both! I'm not the youngest member anymore!! Haha Love You!".
Ella Henderson, who competed on the same series of the X Factor as Union J wrote, "Congratulations @JJUJWorld & @mscaterinalopez on your baby boy! Auntie Ella volunteers for babysitting ☝️ !! Xx."
The first-time parents only announced their baby news in September.
"Guys I want you to be the first to know that I've got some big news," tweeted JJ. "I'm going to be a daddy.... :-) :-) wooop x."
"My girlfriend and I are super super excited and the boys can't wait to be uncles!"