The Virgin tycoon's daughter and her husband Freddie Andrewes revealed their news yesterday.
Holly told the Mail: "Freddie and I are delighted."
Sir Richard, 64, has harboured a desire to become a grandfather ever since he walked his daughter down the aisle in 2001, when he said: "I can't wait - and with luck I'll be one soon."
Holly, 32, is booked to fly alongside her father on Virgin Galactic's first commercial space flight, scheduled for the end of the year.
But she hasn't yet revealed whether her pregnancy will affect her plans to blast into outer space.
Will she board the flight and risk being the first woman to give birth in space? Watch this space (sorry!)
Last year it was revealed that Kate Winslet and her husband Ned Rocknroll's baby son Bear had been promised a free flight into space by Ned's uncle, Sir Richard – when he's old enough.
A source told The Sun: ''Richard has told Kate and Ned they can go up any time and the same goes for their new arrival.''
A ticket on the Virgin Galactic flight costs $200,000 and a host of star-gazing celebrities have already purchased seats.