The announcement comes nearly three weeks after the couple confirmed their engagement last month.
"His Royal Highness Prince Henry of Wales and Ms Meghan Markle will marry on 19th May 2018," the palace said in a statement.
The fifth in line to Britain's throne had revealed his engagement to the 36-year-old actress, best known for her role as Rachel Zane in the legal drama "Suits", last month.
The couple had confirmed that their wedding ceremony will take place some time in May 2018 at St George's Chapel in Windsor Castle.
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Markle, as a Protestant Christian, will be baptised into the Church of England before the ceremony.
She will also begin the process of becoming a British citizen as she prepares for her married life with the 33- year-old prince at their home at Kensington Palace in London.
Earlier this week, it was confirmed that in a break from royal tradition, Markle had been invited by Queen Elizabeth II to spend Christmas with the rest of the royal family at her Sandringham estate.
She will become the first unmarried partner of a royal to attend the traditional celebrations alongside Harry, the 91- year-old Queen's grandson.
Harry will accompany his brother Prince William and sister-in-law Kate Middleton alongside Markle to Sandringham.
"You can expect to see the Duke and Duchess of Cambridge, Prince Harry and Ms Markle at Sandringham on Christmas Day," a Kensington Palace spokesperson had said.
Royal partners have until now had to wait until they were officially married before being invited to spend Christmas with the Queen and the rest of the family at Sandringham.
Harry and Markle are expected to join the Queen from Christmas Eve until Boxing Day, the day after Christmas, before holidaying abroad for the New Year.
They are also understood to be planning to join Markle's mother Doria Ragland in California for part of the time.
Harry and Markle's engagement was announced on November 27, when it was revealed that the prince had proposed to his girlfriend at a quiet dinner earlier in the month.
In his first interview since announcing his engagement to the Markle, Harry told the BBC that he proposed to Markle, three years older to him, earlier that month over a "standard, typical" dinner of roast chicken at their Nottingham Cottage home in Kensington Palace in London.
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