Serena Williams has given birth to a baby girl, the first child for the former world No. 1 tennis player and her fiancé, Reddit co-founder Alexis Ohanian.

The birth of their 6-pound, 13-ounce daughter was announced Friday, Sept. 1, by Ms. Williams’ coach, Patrick Mouratoglou, on Twitter.

The 35-year-old Ms. Williams has not competed since winning the Australian Open in January but has posted several videos to social media showing her hitting balls during her pregnancy.

“Congratulations @SerenaWilliams for your baby girl. I am so happy for you and I feel your emotion,” Mr. Mouratoglou wrote last Friday on Twitter.

“Btw ... I wish you a speedy recovery... we have a lot of work ahead of us,” he added.

Ms. Williams and the baby’s birth quickly became all the buzz at the U.S. Open, a tournament now underway in New York and which Ms. Williams has won six times.

“A baby girl? Well, I hope she doesn’t play tennis,” Garbine Muguruza, who is ranked No. 3 in the world, said with a smile during a news conference.

Ms. Williams’ sister and doubles partner, Venus Williams, romped over another opponent and into the fourth round of the major tennis tournament in Flushing, Queens, shortly after the birth was announced.

She told ESPN she was “super excited” about becoming an aunt, adding, “Words can’t describe.”

Fellow American player Sloane Stephens said she expected to see a lot of the newborn.

“I am very happy for her,” she said. “I cannot wait to see the little baby girl on tour because I am sure she will be around.”

Ms. Williams confirmed her pregnancy in April, hours after triggering frenzied speculation when she accidentally posted a short-lived selfie on social media with the caption: “20 weeks.”

The world’s highest-paid female athlete was about two months pregnant when she captured her 23rd grand slam singles title at the Australian Open, one short of the all-time record held by Australian Margaret Court.

She told Vogue magazine last month about her “outrageous plan” to defend her title in Australia, where the first grand slam of 2018 will be played from Jan. 15 through 28.

Other women have left the tour to have children and returned at a high level, although none has done so at Ms. Williams’ age.

Kim Clijsters of Belgium retired and had a child before coming back at age 26 and winning three grand slam titles. Australians Evonne Goolagong Cawley and Ms. Court also won grand slam titles after having children.

In a recent interview posted on LeBron James’ website Uninterrupted, Ms. Williams said she wants three things for her baby: Equal prize money if her daughter grows up to become an athlete; that she will live a life according to the values that Ms. Williams’ parents instilled in her as a child; and that she will find happiness regardless of circumstances.

Ms. Williams recalled how she was raised not to be overly concerned about money.

“Looking back, we grew up in a two-bedroom house and there were seven people,” she said on the show. “I don’t know how my parents were able to make me feel that way, but they did. It was really special.

“I would love to give my kid the values that my parents gave me. I think that’s most important and I think everything comes after that.”