The dad-of-two was determined to take a father-son selfie, but Buzz was too excited and wanted to play.
Uploading a slightly blurry snap of the pair, Fletcher wrote: "This little man has changed my life in so many ways. Makes me laugh and smile every day.
"Can't believe he's 2! Happy birthday son."
Giovanna Fletcher, who gave birth to the couple's second child Buddy in February 2016, also took the opportunity to reflect on how the couple's life has changed since they started a family two years ago.
"Happy 2nd birthday to my little love Buzz," she wrote alongside a photo of Buzz out on a walk.
"Our world has become a much brighter place since you came along.
"You fill our days with laughter and smiles."
Tom Fletcher also documented Buzz's birthday on Instagram to show what the family of four got up to.
There were of course balloons.
And a card from Buddy to his big brother Buzz.
Mickey Mouse party hats for breakfast.
Mickey Mouse birthday cake.
And playing with one of Buzz's birthday presents - his own football goal.