The happy couple smiled and held hands at the altar in the historic surrounds of St George’s Chapel before exchanging vows in front of a star-studded congregation.
Harry, dressed in military uniform, appeared to say “you look amazing… absolutely gorgeous” to his stunning American bride during the ceremony.
They later shared a tender kiss on the steps of the chapel after becoming husband and wife.
Meghan’s mother Doria Ragland cried tears of joy as her daughter arrived in a dress designed by Clare Waight Keller, artistic director at French fashion house Givenchy.
She walked through the Nave of the stunning chapel on her own, followed by a procession of bridesmaids and pageboys including Prince George and Princess Charlotte.
The bride was met by Prince Charles at the start of the Quire, as her father was forced to miss the event following heart surgery.
Earlier, Harry had arrived at the ceremony with his brother and best man, the Duke of Cambridge, while tens of thousands of people waved union flags as Meghan was driven quickly along the Long Walk to the castle.
The couple will now take on the titles of the Duke and Duchess of Sussex following their marriage.
Approximately 600 guests were in the wedding congregation, including about 30 members of the Royal Family. They included the Queen and the Duke of Edinburgh, 96, who was well enough to attend after undergoing a recent hip operation.
In a moving tribute to Harry’s late mother Diana, Princess of Wales, her sister Lady Jane Fellowes gave a reading during the ceremony.
The presiding bishop of the American Episcopal Church, Bishop Michael Curry, also gave a passionate address, saying: “There’s power in love. Don’t underestimate it. Don’t even over-sentimentalise. There is power, power in love.”
The moving soul classic Stand By Me by Ben E King was performed by Karen Gibson and The Kingdom Choir.
Following the ceremony, the newly-married couple took part in a procession through Windsor in an open-top carriage.
As the horse-drawn carriage returned to Windsor Castle ready for the lunchtime reception, Harry quipped: “I’m ready for a drink now.”
Television star Oprah Winfrey, actor Idris Elba and Earl Spencer, the brother of Diana, Princess of Wales, were among the first guests to arrive for the wedding.
Actor George Clooney and his wife, the human rights lawyer Amal Clooney, soon followed – along with David and Victoria Beckham, tennis champion Serena Williams and music star Sir Elton John.
Ms Markle’s former co-stars from TV drama Suits also attended.
Following the wedding, Meghan’s father Thomas told TMZ he wished his “beautiful” daughter “love and all happiness” after missing the event.
She will make a speech at her wedding reception, along with Harry and Prince Charles, while the Duke of Cambridge will act as compere, Kensington Palace said.
Sir Elton performed at the reception “in recognition of the close connection he has with Prince Harry and his family”, the palace added.
Harry will wear a ring as a married man – not a given for male members of the Royal Family.
The 33-year-old prince and Ms Markle, 36, became engaged following a whirlwind 16-month romance after going on a blind date in London.
She wed her first husband, film producer Trevor Engelson, in 2011 – but the pair divorced less than two years later.
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Royal wedding: Who’s Who
:: See all of the guests as they arrived at the royal wedding – use our exclusive, interactive Who’s Who feature on the Sky News app and website.
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