The McFly singer announced the arrival of his son on 16 February to his fans on Twitter.
"Completely overwhelmed with love for our second son Buddy, and can’t wait for him to meet his big brother," the 30-year-old tweeted.
"Thanks for the lovely messages."
Completely overwhelmed with love for our second son Buddy, and can’t wait for him to meet his big brother. Thanks for the lovely messages. X— Tom Fletcher (@tommcfly) February 16, 2016
Giovanna Fletcher also took to Instagram to announce the birth, with a photo of the blue sky.
"What a beautiful day to be born," she wrote. "Welcome to the world Buddy Bob Fletcher."
The couple, who have not yet shared a photo of their newborn son, are also parents to two-year-old Buzz.
They announced they were expecting their second child together in September 2015 with a videogame creation.