Kensington Palace said the couple are "hugely grateful for the many good wishes they have received".
The chapel holds about 800 people, making it a more intimate setting than the Duke and Duchess of Cambridge's wedding in Westminster Abbey.
The couple will then return to a reception for guests from the congregation at St. George's Hall.
Markle will be baptised into the Church of England and confirmed before the wedding.
The wedding will take place just a month after the Duke and Duchess of Cambridge are expected to welcome their third child.
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