The Queen is said to be "delighted" after learning she is to become a great-grandmother for the first time.
Buckingham Palace said Princess Anne's son Peter Phillips and his Canadian-born wife Autumn were expecting their first child in December.
Mr Phillips, the Queen's eldest grandson and 11th in line to the throne, met his wife while working at the Montreal Grand Prix in 2003.
They were married at Windsor Castle in May 2008.
A Palace statement said: "Peter and Autumn Phillips are delighted to confirm they are expecting a baby in December.
"The Queen and Duke of Edinburgh, as well as Autumn's family, have been informed and are delighted with the news."
Mrs Phillips, a former Roman Catholic, was accepted into the Church of England shortly before their wedding.
Her husband would have had to give up his right to the throne had she not done so.
The couple were caught in controversy two years ago over their wedding photographs which were bought up exclusively by a glossy magazine for a reported £500,000.