The 35-year-old American, who is engaged to Reddit co-founder Alexis Ohanian, 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," Mouratoglou wrote.
"Btw ... I wish you a speedy recovery... we have a lot of work ahead of us," he added.
Williams has dominated the sport for the past decade and is one grand slam short of Australian Margaret Court's record of 24 major titles.
She 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".
Williams, 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.
She told Vogue magazine last month about her "outrageous plan" to defend her title in Australia, where the year's first grand slam will be played from Jan. 15-28.
Other women have left the tour to have children and returned at a high level, although none has done so at 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 Court also won grand slam titles after having children.
source: news.abs-cbn.com
