The couple announced the birth on Twitter today and they've given their baby an unusual nameSailing star Sir Ben Ainslie is celebrating the birth of his first child with wife Georgie Thompson - named after a goddess of war.
The birth was announced on Twitter by the 39-year-old's sailing team, Land Rover BAR, with a black and white photo of the Olympian with the sports presenter, 38, and their daughter Bellatrix.
Land Rover BAR said: "Congratulations @AinslieBen @OfficiallyGT on the birth of your beautiful baby Bellatrix £BringTheBabyHome".
Sir Ben responded: "proudestday".Congratulations @AinslieBen @OfficiallyGT on the birth of your beautiful baby Bellatrix #BringTheBabyHome pic.twitter.com/J2ckTfNKQL— Land Rover BAR (@LandRoverBAR) 21 July 2016
The four-time Olympic champion, who also has a silver medal, is making his final preparations ahead of the ACWS event which gives the six teams a chance to win points ahead of the finals in Bermuda next year.
The teams compete in wing-sailed catamarans which "fly" over the water on hydrofoils.
Sir Ben said: "We had our first baby last weekend so are absolutely delighted with that, we managed to get Georgie and the baby back home last night so they are well looked after.
"She is called Bellatrix, which is something to do with being the Goddess of War, so hopefully she will be behind the team when we are in Bermuda next year."
He said: "We hope to repeat that again this next year, it's the last time we get to race in the UK before the cup next in Bermuda so the guys are really fired up to try and put on a good show, we have the weather forecast and some great teams here, should be some fantastic racing."
The Land Rover BAR team, in second place in the series, is hoping to be the first British team to win the America's Cup in its 165-year history.
The Duke and Duchess of Cambridge were special guests at last year's event which attracted 250,000 spectators but was curtailed by heavy rain, and will again be watching the racing on Sunday before attending the prize-giving.
Kate, who is the patron of the 1851 Trust, the Land Rover BAR team charity to encourage young people into sailing and the maritime industry, wrote in a foreword to the ACWS programme: "I am sure you will join William and me in wishing Sir Ben and the team the best of luck. We all remain hopeful that it might be the year we see the America's Cup coming home after 165 years."
The America's Cup dates back to 1851 when a group of US businessmen visiting for Prince Albert's Great Exhibition challenged a British team to a race around the Isle of Wight, which they won, and the British have since failed to win back the trophy, affectionately known as the "Auld Mug".