Their son is understood to have been born in London last week.
The couple, both 32, already have two daughters.
The news was revealed to the Scottish Sun by Sir Andy's grandfather Roy Erskine, 88, who told the newspaper: "It's a wee boy, I don't know his name yet. I've seen photos. They're doing fine."
Judy Murray said: "It's lovely news. It's lovely to have a little boy to go with the two little girls.
"I'll leave Andy and Kim to fill in any further details but yeah, a lovely, happy, healthy baby boy."