The Australian great and her husband, golf professional Garry Kissick, reported in an Instagram post on Tuesday they had become the proud parents of a "beautiful boy".
"Welcome to the world, Hayden!," their post read, accompanied by a picture of the new arrival wrapped in a blanket.
The news was acclaimed at Wimbledon, where Barty had been feted two years and one day previously after achieving her dream of winning the singles title.
Ons Jabeur, last year's losing finalist, was delighted for the player she so admired, having said recently she felt Barty would have won 20 grand slams if she had continued her career.
Now the Tunisian wants to see Barty make a comeback like the one announced last week by another former world No.1 Caroline Wozniacki, who gave birth to her second child in October.
"Fantastic news. I'm very happy for her that she had a baby boy. I'm very happy for her because this is something that I want to have, a family," world No.6 Jabeur said after her first-round victory over Poland's Magdalena Frech.
"I'm sure she's enjoying being a mum right now rather than being on a tennis court waiting to play at Wimbledon.
"I hope that she will change her mind like Wozniacki and comes back maybe in one or two years."
World No.2 Aryna Sabalenka, who this year succeeded Barty as Australian Open champion, added: "I'm super-happy for her. I wish her all the best in her new chapter of her life. I think she's really enjoying it.
"I really miss Ashleigh on tour. I really enjoyed our matches against each other, all our battles, but she made her decision and I really respect it."
Asked about a Barty comeback, Sabalenka said: "She has everything to come back. She's very talented. I feel like she already made it once.
"If she's going to decide to come back playing tennis, she's going to do well."
Last year, Barty caused a sensation by announcing her retirement from the sport in March, less than two months after winning the Australian Open in Melbourne and when she was still a completely dominant figure at the top of the game.
She married Kissick in July last year in Queensland, and in January announced her pregnancy, declaring: "2023 set to be the best year yet".
Craig Tiley, CEO of Tennis Australia, led the wave of congratulations from within the sport for the popular Barty, calling the arrival of baby Hayden "wonderful news".
There has been plenty of speculation over whether Barty, now 27, might decide to make a comeback at some point.
And the guessing games are set to continue over whether the woman who lifted three of the slams - French Open (2020), Wimbledon (2021) and Australian Open (2022) - may one day join the band of successful tennis mums.
Down the years, that esteemed list has included Kim Clijsters, Serena Williams, Victoria Azarenka and Barty's own heroine, Evonne Goolagong-Cawley, who back in 1980 became the first mother to win the Wimbledon singles for 66 years.
When asked about the prospect of one day returning to the sport, Barty said after her retirement: "I'd say you never say never. I'd say the door is closed, but it's not padlocked."
9°C