The Dunblane tennis star’s wife is understood to have given birth on Sunday night, the BBC reported.
A formal announcement is expected shortly.
The birth of their first child comes after a momentous 12-month period forMurray, the British number one and a double grand slam winner.
The long-term couple, who live in Surrey and are both 28, married in Murray’s home town of Dunblane in April last year, cheered on by a large crowd of well-wishers.
Kim’s pregnancy was confirmed publicly in August after they had told family and friends the news, following the 12-week scan.
On the tennis court in 2015, Murray reached the semi-finals of the French Open and Wimbledon, and won his first titles on clay.
He went on to round off the year by steering Great Britain to its first Davis Cup title in almost 80 years. He was also crowned BBC Sports Personality Of The Year for a second time.
As well as making it to the Australian Open final, he watched his brother Jamie become the first Briton to win the Australian Open men’s doubles title in more than 80 years.
Murray spoke ahead of the Australian Open about the upcoming birth.
“Just now it’s a big change coming. It’s very, very exciting,” he said.
The Scot made it clear in January that he would have cut short his first grand slam of the year and flown home if the baby had arrived earlier than expected.
Confirming he would even have quit the tournament with one match left to play, he added: “For me, my child is more important to me, and my wife is more important to me than a tennis match.”
Memorably, Murray did make it to the final and tearfully told Kim he would be on “the next flight home” after being beaten to the title by Novak Djokovic.
Murray’s father-in-law Nigel Sears had been rushed to hospital during the tournament after collapsing at the Rod Laver Arena in Melbourne while he watched Ana Ivanovic, whom he coaches. The 58-year-old was later cleared to fly back to the UK and Murray said previously he would have pulled out of the tournament if there had been any doubts about his father-in-law’s health.
Speaking to the crowd after the defeat, Murray gave a message to Kim, who was “watching back home”.
He said: “You have been a legend the last two weeks, thank you so much for all of your support. I’ll be on the next flight home.”
Well-known names from the worlds of sport and politics were quick off the markto offer the couple their congratulations.
Scotland’s First Minister Nicola Sturgeon tweeted: “Lovely news. Congratulations to {M0andy-murray and Kim on the birth of their daughter. Wishing every happiness.”
Sports broadcaster Gabby Logan said: “Kim and Andy Murray have had a baby girl -huge congrats.”
And in a note to Murray’s mother Judy, the presenter added: “@judmoo – great news for Fed Cup team 2036…”
Presenter Annabel Croft, a former British number one tennis star, wrote: “Congratulations Kim & {M0andy-murray on the birth of their baby daughter. Fantastic news.”
The SNP’s leader at Westminster Angus Robertson said: “Congratulations to {M0andy-murray and Kim Sears on the birth of their daughter.”
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