American tennis star Serena Williams has announced the name and released first pictures of her baby girl, revealing they had spent a week in the hospital, following the September 1 birth in Florida, because of unspecified complications.

"Meet Alexis Olympia Ohanian Jr," the former world No. 1 and 23-time Grand Slam champion said in postings on her social media sites, that included a video diary of her pregnancy.

Williams, 35, who is engaged to reddit co-founder Alexis Ohanian, said the baby weighed 3.1 kilograms.

"So we're leaving the hospital after six days. It's been a long time. We had a lot of complications, but look what we got!" Williams said in the video, cradling the baby.

The video showed Williams dancing, hitting tennis balls as her pregnancy progressed, selfies of her expanding belly, and home video of the couple putting together the baby's cot.

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

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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 has not competed since announcing her pregnancy but she told Vogue magazine last month she intends to defend her title next year in Australia, where the year's first Grand Slam will be played from January 15-28.

Reddit was among the first to congratulate the couple on Wednesday.

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Reuters