A statement said the musician and her Qatari businessman husband, Wissam Al Mana, were “thrilled” to welcome the infant, Eissa Al Mana.
“Janet had a stress-free healthy delivery and is resting comfortably,” the publicist added.
Speculation about her pregnancy surfaced last April when she postponed her Unbreakable tour.
She posted a video on Twitter at the time in which she told fans that she was postponing the tour because “there’s been a sudden change”.
“I thought it was important that you be the first to know,” she said, adding: “Please, if you can try and understand that it’s important that I do this now.”
She said she wanted to focus on planning a family with her husband, whom she wed in 2012.
Jackson had earlier been spotted in London shopping for baby essentials.