Williams, who will turn 36 later this month, was admitted to the St Mary's Medical Center in West Palm Beach, Florida on Wednesday before going into labor overnight.
There was no immediate confirmation of the birth from Williams' representatives.
Elder sister Venus Williams described herself as "super excited" after being informed of the reports concerning the baby as she walked on to the court for her third-round match at the US Open in New York.
"I'm definitely available to answer questions about tennis. That's all right now," Venus told reporters.
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Earlier, a producer with the Florida-based WPBF television station cited hospital sources as saying Williams' daughter weighed in at six pounds and 13 ounces (3.09 kilograms). Celebrity magazine US Weekly cited an unnamed source close to the tennis star confirming the birth.
Williams, who is engaged to Reddit co-founder Alexis Ohanian, was swiftly greeted with an avalanche of congratulations from well-wishers.
"Congrats Serena!!! So much joy for you!!!" Spanish star Rafa Nadal wrote on Twitter.
Williams' coach Patrick Mouratoglou added on Twitter: "Congratulations @SerenaWilliams for your baby girl. I am so happy for you and I feel your emotion. Recover well & enjoy without limitation."
US tennis legend Chris Evert meanwhile chimed: "I'm so thrilled for her. And what a role model she's going to be for her daughter."
Media reports said 23-time Grand Slam singles champion Serena -- who revealed she was pregnant in April -- was induced overnight Thursday.
"Hello to the future queen of tennis," one post on Twitter read. "A future champion is born," added another.
Those sentiments sparked light-hearted alarm for Spanish star Garbine Muguruza. Told that Williams' baby is a girl, Muguruza replied: "Well, I hope she doesn't play tennis."
- 'Outrageous' goal -
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Williams has vowed to return to competitive tennis in January to defend her Australian Open title, which she won while newly pregnant.
Williams last month told Vogue in a wide-ranging interview that she had set herself a goal of returning to play in Melbourne at next year's Open.
Williams' coach Mouratoglou meanwhile joked yesterday that he expected to hold the tennis star to her word.
"Btw @serenawilliams I wish you a speedy recovery... We have a lot of work ahead of us," Mouratoglou wrote in a Twitter post.
Williams also revealed in her Vogue interview she had long suspected she would give birth to a girl.
"Two weeks after we found out (about the pregnancy), I played the Australian Open. I told Alexis it has to be a girl because there I was playing in 100-degree weather, and that baby never gave me any trouble. Ride or die. Women are tough that way," Williams told the magazine.
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