Tennis player Andy, 28, will become a father for the first time, his agent has confirmed to BBC News.
The Sun reports that 27-year-old Kim recently had her 12-week scan, with the baby due in February.
World No. 3 Andy broke the news to his tennis coach mum and Strictly Come Dancing star Judy, just a few months after she said in an interview that she was dreaming of becoming a grandmother.
Andy and Kim, who have been together for nine years, married in Scotland on 11 April at Andy's own five-star Cromlix House Hotel near Dunblane.
In 2013, former Wimbledon champion Andy said in his autobiography that having two dogs felt like having to look after children.
"It is not the same as having kids - or at least I don't think it is - but that's sometimes what it feels like."
Try Reveal's digital edition on iPhone & iPad. Subscribe now & never miss an issue!