Serena Williams, 35, has welcomed her first child, a daughter, but the new mum will have more on her mind than nappies and feeding times if her coach has any say in the matter.

While the tennis titan’s friends, Hollywood luminaries and fellow centre court stars inundated the champion with congratulations, coach Patrick Mouratoglou was focused on getting back to the business of building on Ms Williams’ already stellar record.

“I wish you a speedy recovery … we have a lot of work ahead of us,” tweeted the hard-driving Frenchman, apparently after having second thoughts about an initial tweet urging the jubilant mother to enjoy her baby “without limitation.”

The 35-year-old has not played competitive tennis since January, when she defeated sister Venus while one month pregnant to claim the Australian Open women’s crown.

Local news network CBS 12 reported that Williams checked into St Mary’s Medical Centre in Palm Beach, Florida, on Wednesday (local time) and had the entire first floor cleared for security reasons.

Williams was induced on Thursday (local time), according to CBS 12, and gave birth to a baby girl weighing in at 3.09kg.

The US Open Tennis official Twitter account tweeted a video message of congratulations to the sporting star on Friday which included heartfelt tributes from tennis pros around the world.

Pop queen Beyonce was among the first to jump onto social media to congratulate the first-time mother, followed by grand slam champion Rafael Nadal who tweeted: “Congrats Serena!!! So much joy for you!!!”

Her sister, Venus, currently playing in the US Open, told ESPN’s Pam Shriver before her third-round match that she was “super excited” about becoming an aunt.

“Words can’t describe,” she said.

Fellow commentator Chris Evert said that she was “thrilled” for her, saying what a “role model she’s going to be for that daughter”.

“I told Serena this: It’s a love you’ve never felt before – and I know she’s probably experiencing that right now,” she said.

Congratulations to @serenawilliams for giving birth to a baby girl!

Sending you ❤️ from your friends & family at the #USOpen and @WTA! pic.twitter.com/zv8HW0dDTN

— US Open Tennis (@usopen) September 1, 2017

Stacey Allaster, chief executive of the United States Tennis Association, said: “Hey Serena, welcome to the best club in the world: motherhood. Can’t wait to see you, a mum, and your precious little healthy baby. Congrats!”

Serena accidentally revealed her pregnancy in April when she posted a picture of herself in a yellow swimsuit, showing off a prominent bump, on the social media app Snapchat.

It came with the caption ”20 weeks”, but was then deleted without explanation before official confirmation came several hours later.

Williams, who is engaged to co-founder of social news website Reddit, Alexis Ohanian, 34, has spoken about her pregnancy recently in high-end magazines Vanity Fair and Vogue.

Vogue posted a tribute to the new mother and quoted her interview where she said: “Two weeks after we found out (about the pregnancy), I played the Australian Open”.

For her 23rd grand slam title, she beat her sister in the final in Melbourne in January.

Congratulations @SerenaWilliams! The tennis star has given birth to her first child. https://t.co/YdnqXcnPxC

— Vogue Magazine (@voguemagazine) September 1, 2017

“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.”

Check out my Vanity Fair Cover. Question- what do u guys think boy or girl? I'm waiting to find out but would love to hear your thoughts. pic.twitter.com/Nnq4VKCu8N

— Serena Williams (@serenawilliams) June 27, 2017

Last month, the 23-time Grand Slam winner hosted a 50s-themed baby shower, with stars such as Eva Longoria, Ciara, Destiny’s Child star Kelly Rowland and La La Anthony among the guests.

When you and your crew go so far back to the 50's. Even then they had your back. @evalongoria… https://t.co/29Vojbz4C0

— Serena Williams (@serenawilliams) August 6, 2017

—with AAP