No doubt the first-time parents are enjoying their new company and their little bundle of joy.
"I've been having a cuddle with Buzz for about an hour," posted Tom. "Best cuddle of my life. Ever!"
The All About You singer, who makes up one quarter of Brit Award winning band McFly, was so excited about his new role that he changed his Twitter bio line to an excited "Dad!"
Tom has been embracing the challenges of becoming a father, writing, "Oh so this is what 'tired' really feels like…blimey…" two days after Buzz was born.
Tom and Giovanna are clearly over the moon and have made no secret of their love for their baby boy.
The Italian beauty announced the couple's happy news on Twitter, writing, "THRILLED to announce the safe arrival of our little BOY! Born last night at 7pm. I can't stop staring at and kissing him! I'm in love! Xxx."
In her latest blog post, Giovanna shared just how excited she was to meet her unborn baby, who the couple had nicknamed "Crumb" and hadn't known his or her gender.
"And now we've arrived at 37 weeks," she posted. "From this point on Crumb can arrive whenever he/she chooses. It's mindboggling to think that the little human I've been growing for the last eight and a half months is about to come out and meet us. I can't wait!"