The pair, whose engagement was confirmed last month, will tie the knot at St George's Chapel, inside the grounds of Windsor Castle, one of the Queen's main residences.
The 15th century building has been the location of many royal ceremonies, weddings and burials and is more intimate than Westminster Abbey, where Harry's older brother William married Kate Middleton in 2011.
The Royal Family has said it will pay for the wedding out of their private funds.
But the event will be on a Saturday and the public will miss out on an extra Bank Holiday.
The 33-year-old prince, who is fifth in line to the throne, and the 36-year-old American actress met through a mutual friend in 2016 and managed to keep their relationship secret from the media for several months.
The wedding date presents a potential clash for Prince William, however. William is president of the English Football Association and 19 May is the date of the FA Cup final, one of the biggest games of the year.
He attended this year's match and presented a trophy to the winner, Arsenal.
Markle is set to appear at church with the royals on Christmas Day at Sandringham.
She has announced that she is to quit acting to focus on her royal duties.
The producers of her hit TV show, Suits, have confirmed they are writing out her character at the end of the seventh series.
Well known for her philanthropy and activism, she served as a counsellor for international charity One Young World and as a global ambassador for World Vision Canada.
Additional reporting by PA
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