The news comes one month after Sam's sister Holly confirmed that she is expecting twins with her husband Fred Andrews. Both siblings are set to become first-time parents within a few weeks of each other.
It was Richard who announced Sam's happy news on his Virgin blog, under a post titled 'Becoming proud grandparents – again'.
Sam retweeted the post, before writing: "Couldn't be happier about becoming a father. Going to be my biggest adventure. Can't wait ;)."
In his heartfelt message, Sir Richard wrote, "It's another magical moment for the whole family. Joan and I, along with Isabella's parents Mary Gaye and Jo, can't wait to become proud grandparents.
Couldn't be happier about becoming a father. Going to be my biggest adventure. Can't wait :) http://t.co/GTEyyOpKH6— sambranson (@sambranson) septiembre 9, 2014
"Bellie's due date is only a few weeks behind Holly's, so we are looking forward to welcoming three grandchildren to the family in 2015.
"We're incredibly fortunate and everyone is very excited.
"Holly and Sam have always been the closest of siblings, which has brought so much joy to Joan and I as parents."
The English business magnate added, "I'm sure that our grandkids will be just as close or even closer if that's possible. As Bellie said, 'Such lucky cousins they will be!' Sam's family lives next to Holly's family in Oxford and we're all looking forward to watching the children grow up together.
"People often ask why I always have a huge grin on my face: the answer is the love and support of my family. Now we're going to have some grandchildren to adore, the grin will be even wider!"
Sam and Isabella – the older sister of Cressida Bonas – were married in South Africa in March 2013, in a romantic ceremony held at Sir Richard’s private game reserve.
"The ceremony was so emotional and beautiful," guest Princess Beatrice told HELLO! afterwards. "Sam did so well not crying – but none of the rest of us can say the same. There was hardly any point wearing make-up."