Harry and Meghan are preparing to welcome a brother or sister for their young son Archie Mountbatten-Windsor, who turns two in May.
A Buckingham Palace spokesman said the Queen and Prince Philip, and the entire royal family were delighted by the news and wished the couple well.
The baby news comes after the duchess suffered a heartbreaking miscarriage in the summer of 2020, and just days after she won a privacy case against Associated Newspapers Limited.
A spokesperson for Meghan and Harry said: "We can confirm that Archie is going to be a big brother.
"The Duke and Duchess of Sussex are overjoyed to be expecting their second child."
The couple shared a black and white picture of themselves under a tree with Harry resting his hand on Meghan's head as she lies in his lap cradling her bump.
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Meghan revealed her miscarriage in November last year in a deeply personal article for the New York Times, writing: "I knew, as I clutched my firstborn child, that I was losing my second."
Harry, 36, and Meghan, 39, quit their roles as senior working royals in March 2020 in a quest for personal and financial freedom, and now live in California.
The Valentine's Day announcement came just five days after the royal family celebrated the arrival of Princess Eugenie's first child, a boy.
Baby Sussex will be the Queen and the Duke of Edinburgh's 10th or 11th great-grandchild, depending on whether he or she arrives before or after Zara Tindall's baby, which is also due in 2021.
In October, Meghan's potential privacy trial at the High Court was postponed from January 2021 to the autumn for a confidential reason, leading to speculation Meghan might be expecting a baby.
A month later, Meghan wrote of experiencing an "almost unbearable grief" after losing a child in a miscarriage last summer.
In 2019, proud father Harry announced the arrival of their first-born Archie to a media pool, then later held his newborn son in his arms, with Meghan at his side, for his public debut at Windsor Castle.
The new baby will still be eighth in line to the throne and the Prince of Wales's fifth grandchild.