The baby weighs a healthy 8lb 10oz and mum and little one are well and happy.
"Andy and Kim had a daughter in the early hours of Sunday morning and the family are doing well."
Last month, Andy revealed he was switching his priorities so his family came first and tennis second.
"My child is more important to me, and my wife is more important to me, than a tennis match,” he said. "It's a big change for me and my wife, but that's the current priority and I'll see after that.
"I have no idea how that will change things. I still love tennis."
Andy and Kim married last April in his home town of Dunblane and announced she was pregnant three months later.
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