The palace said the couple has "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 royal baby will be seventh in line to the British throne. It will be behind grandfather Prince Charles; uncle Prince William; cousins Prince George, Princess Charlotte and Prince Louis; and dad Prince Harry.
The parents-to-be were married on May 19, 2018, at Windsor Castle. Upon marriage, Prince Harry and Meghan Markle took on the titles of Duke and Duchess of Sussex.
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Before meeting her future husband, Markle was an actress, best known for playing Rachel Zane on the show Suits, as well as a trendsetter and an activist.
The royal couple has many causes dear to their hearts. When they got married they asked for donations in lieu of presents, and their charities of choice included those that combat HIV, homelessness and lack of access to sanitary pads for women.
The pair lives in Kensington Palace with their two dogs.
The Associated Press and ABC News contributed to this report.