The Australian great and her husband, golf professional Garry Kissick, reported that they were the proud parents of a "beautiful boy" in an Instagram post on Tuesday.
"Welcome to the world, Hayden!," their post read, accompanied by a picture of the new arrival wrapped in a blanket.
The news was acclaimed during the day by her old friends at Wimbledon where Barty, a three-time grand slam champion, had been feted just two years and one day previously for achieving her dream of winning the singles title.
Tunisian pioneer Jabeur, last year's finalist, was delighted for the player she so admired, having said recently that she felt Barty would have won 20 grand slams if she had continued her career.
Now she wants to see her make a comeback like the one that former world No.1 Caroline Wozniacki, who gave birth to her second child in October, announced last week.
"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," said the world No.6 Jabeur after her first round victory over Poland's Magdalena Frech.
"I'm sure she's enjoying being a mom right now rather than being on a tennis court waiting to play at Wimbledon," she added with a smile.
"I hope that she will change her mind like Wozniacki and comes back maybe in one or two years."
Last year, Barty had caused a sensation by announcing her retirement from the sport in March less than two months after she'd won the Australian Open in Melbourne, breaking a 44-year drought for Australian women players, and when she was still a completely dominant figure at the top of the game.
Barty then got married to 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 it "wonderful news".
Inevitably, though, since her retirement as the world No.1 at the peak of her powers, there has been speculation over whether Barty, now 27, might decide to make a comeback at some point.
And, doubtless, the guessing games will still 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 became the first mother to win the Wimbledon singles for 66 years back in 1980.
When asked about the prospect of one day returning to the sport herself, Barty said after her retirement: "I'd say you never say never. I'd say the door is closed, but it's not padlocked.
"I'm never one to absolutely say never, never, never. But, yeah, it feels like it's closed."
