The new daddy captioned the image – in which he has his eyes closed and is flexing his muscles for the camera – "Tummy time with Dad".
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"Tummy time with Dad," Tom captioned this sweet image
Little Buzz, who is dressed in a long-sleeved white romper suit, looks to be thriving since coming home from hospital on March 27.
On that day Tom tweeted his relief to be bringing his son and wife home two weeks after Giovanna gave birth.
“Buzz is 2 weeks old today and we're all looking forward to finally getting out of the hospital this afternoon! Whoop!!!!” he said.
The new dad didn't disclose what medical condition kept the family in hospital, but did let his fans know that their little one was "doing fine".
The family are settling into home life after leaving hospital with Buzz on March 27.
Formerly of just McFly and now balancing life with McBusted, Tom has been keeping his more than 1.29 million followers up to date with pictures and funny comments.
And there was also his sweet video, From Bump To Buzz - which shows him singing a brand new tune alongside a collage of snapshots which show his wife’s belly growing throughout pregnancy.
The clip made it onto US TV and went viral, with stars such as Russell Crowe sharing it on the web.
When Giovanna found out she shared her excitement, writing: “Erm... THE Russell Crowe just tweeted a link to Bump to Buzz.......... Amazing!”