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 five-metre veil 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.
Mr Markle, 73, reportedly watched the ceremony from California.
He told the US celebrity website, TMZ: "My baby looks beautiful and she looks very happy."
In her vows, Ms Markle did not promise to "obey" her husband, while the prince has broken with royal tradition by choosing to wear a wedding ring.
Prince Harry's ring is a platinum band with a textured finish and Ms Markle's has been made from a piece of Welsh gold.
During the service, the couple pledged themselves to one another, saying: "For better, for worse, for richer, for poorer, in sickness and in health, to love and to cherish, 'til death us do part."
'Power in love'
The Most Rev Bishop Michael Curry, the president of the US Episcopal Church, gave an address, the Rt Rev David Conner, Dean of Windsor, conducted the service and the Archbishop of Canterbury, the Most Rev Justin Welby, officiated.
"There's power, power in love," Bishop Curry said.
"If you don't believe me think about a time when you first fell in love. The whole world seemed to centre around you and your beloved. Well... there's power, power in love."
Lady Jane Fellowes, the sister of Prince Harry's late mother, Diana, Princess of Wales, gave a reading.
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.
He was accompanied by 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.
After the service, the duke and duchess travelled through Windsor along a route lined by tens of thousands of well-wishers.
The Royal Borough of Windsor and Maidenhead said more than 100,000 people visited the town on Saturday.
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