The Duke and Duchess of Sussex are expecting a baby in the spring, Kensington Palace has announced.
The palace said they were "delighted to share the happy news with the public".
The baby will be the seventh in line to the throne.
Doria Ragland, the mother of the duchess, is "very happy about this lovely news" and "looks forward to welcoming her first grandchild".
In a statement, Kensington Palace said: "Their Royal Highnesses The Duke and Duchess of Sussex are very pleased to announce that The Duchess of Sussex is expecting a baby in the Spring of 2019.
"Their Royal Highnesses have appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public."
The infant will be the Prince of Wales's fourth grandchild and be a cousin of the Duke and Duchess of Cambridge's three children, Prince George, Princess Charlotte and Prince Louis.
The baby will not be a prince or a princess unless the Queen steps in to issue a Letters Patent ahead of the birth.
Otherwise a son would be known as Earl of Dumbarton - because a first son of a duke is allowed to use one of his father's other lesser titles as a courtesy title.
Harry was also made the Earl of Dumbarton on the morning of his wedding, as well as being given a dukedom.
A daughter would be Lady Mountbatten-Windsor.
Both Harry and Meghan have spoken openly about wanting to start a family.
The topic cropped up in their engagement interview, with Harry, saying: "Hopefully we'll start a family in the near future."
The Duchess of Sussex may follow her sister-in-law's lead and give birth at the private Lindo Wing in St Mary's Hospital, Paddington, where the Duchess of Cambridge had three successful deliveries.
Prince Harry was born there in 1984 and it is close to Kensington Palace and well practiced at dealing with royal births, and the publicity surrounding them.
The couple could apply for their child to have dual US-UK citizenship. Meghan is planning to become a British citizen - but it is not known whether she will hold dual nationality, and at present is still a US citizen.
Harry, 34, and 37-year-old Meghan became engaged following a whirlwind 16-month romance after going on a blind date in London.
The prince has told how "all the stars were aligned" when they met.
"This beautiful woman just sort of literally tripped and fell into my life, I fell into her life," he said when their engagement was announced last November.
They wed in a glittering ceremony in St George's Chapel, Windsor Castle, just five months ago.
Speaking at an event to tackle loneliness, Theresa May said the couple's news was "wonderful" and she was "very happy for them".
Earlier on Monday the Prime Minister wished Meghan and Harry "all the best" and sent her "warmest congratulations" in a tweet.
Many others took to Twitter to congratulate the Royals.
Justin Welby, the Archbishop of Canterbury said he would "pray" for the couple.
While Mayor of London Sadiq Khan congratulated the soon-to-be-parents.
The Invictus Games, a multi-sport competition for injured veterans which was created by Prince Harry, congratulated the pair who will attend numerous events when the sports kicks off in Sydney this week.
Australian Prime Minister Scott Morrison said that he was "thrilled" for the Duke and Duchess and was "looking forward to sharing in the joy" during their time in Australia.
The Royal Air Force also congratulated the pair.