The couple exchanged vows and rings before the Queen and 600 guests at St George's Chapel. Wearing a dress by British designer Clare Waight Keller, Ms Markle was met by Prince Charles, who walked her down the aisle.
Following their marriage, the couple will be known as the Duke and Duchess of Sussex. Among the guests were Oprah Winfrey, George and Amal Clooney, David and Victoria Beckham and Sir Elton John. Ms Markle had 10 bridesmaids and pageboys - including Prince George and Princess Charlotte. She wore Queen Mary's diamond bandeau tiara, loaned to her by the Queen.
Her sculpted white dress was designed by Ms Waight Keller for French fashion house Givenchy. The look was completed with a veil measuring 5m and embroidered with the flowers of each country in the Commonwealth.
Prince Charles walked Ms Markle down the aisle, after her father, Thomas, was unable to attend for health reasons. Karen Gibson and The Kingdom Choir performed Ben E King's soul classic Stand By Me during the service.
As the bride and groom signed the register, 19-year-old cellist Sheku Kanneh-Mason - who won the 2016 BBC's Young Musician - performed three pieces - by Faure, Schubert and Maria Theresia von Paradis, with musicians from the BBC National Orchestra of Wales, the English Chamber Orchestra and the Philharmonia.
The gospel choir also performed Etta James' uplifting version of Amen/This Little Light of Mine as the newlyweds left the chapel. Politicians, including Prime Minister Theresa May, were not invited, as it is not a state event.