Prince Edward and his wife, the Countess of Wessex, are expecting their second child in December. Sophie, 42, and Edward - who have a three-year-old daughter Louise - are said to be "delighted" with the news.
Queen Elizabeth and Prince Philip - for who the baby will be their eighth grandchild - are also said to be "thrilled."
The couple was believed to have almost given up hope of having another child after undergoing years of fertility treatment, following the birth of Louise.
Sophie lost her first baby and almost died in 2001 when she suffered an ectopic pregnancy - where the fetus grows outside the womb - and had to be airlifted to the hospital. She subsequently lost the baby.
When Louise was born the countess had to undergo an emergency caesarean after suffering stomach pains.
A friend of the couple said: "Louise is adored by everyone and is the apple of the queen's eye. Sophie and Edward felt they were lucky to have a beautiful child already. Having another baby was in the lap of the gods."
Sophie beamed as she carried out an official engagement at the Royal Agricultural Show, in Warwickshire.
Her spokesman said: "She is not putting her feet up. She is going to carry on official engagements as long as she can. She is feeling great and is completely over the moon."
"I don't know about morning sickness. She looks great and is smiling from ear-to-ear."
The baby will be the ninth in line to the British throne and will have the title Viscount Severn.