The celebrity chef, 57, strongly suggested that Jesse James Ramsay would be his last child, posting on social media: "3 boys, 3 girls.... Done."
Cookery book author Tana, 49, married Ramsay in 1996.
Ramsay posted pictures of Jesse and Tana in hospital on Saturday night.
The baby boy, wearing a pink hat, can be seen in his mother's arms in three images, one of which shows his father kissing him on the head.
Ramsay, who celebrated his birthday on Wednesday, wrote on Instagram: "What an amazing birthday present, please welcome Jesse James Ramsay, 7lbs 10oz whopper!!
"One more bundle of love to the Ramsay brigade!! 3 boys, 3 girls.... Done."
It is unclear exactly when Jesse was born.
The couple are already parents to Megan, the eldest, who is now in her mid-20s; twins Jack and Holly, Matilda "Tilly" and Oscar.
In 2016, before the birth of Oscar,Ramsay announced that Tana had had a miscarriage.
In response to his post about the birth of Jesse, Ramsay received a string of congratulatory messages from celebrity friends, including Hollywood star Jeremy Renner, TV chefs James Martin and Gino D'Acampo, Top Gear star Paddy McGuinness and Strictly Come Dancing professional Amy Dowden.
Former Chelsea FC manager and ex-England footballer Frank Lampard wrote: "Congratulations mate!"
Gordon Ramsay has announced the birth of his sixth child, as he and his wife Tana welcome a 7lbs 10oz "whopper" to the family.