Ms Markle has 10 bridesmaids and pageboys - including Prince George and Princess Charlotte .
Wearing a dress by British designer Clare Waight Keller, Ms Markle was met by Prince Charles, who walked her down the aisle.
Among the 600 guests are Oprah Winfrey, George and Amal Clooney, David and Victoria Beckham and Sir Elton John.
Prince Harry has been made the Duke of Sussex by the Queen, with Ms Markle becoming the Duchess of Sussex.
The prince, who is sixth in line to the throne, also received the titles Earl of Dumbarton and Baron Kilkeel.
Thousands of well-wishers are in Windsor, while hundreds more camped out overnight to secure the best viewing spot.
Prince Charles walked Ms Markle down the aisle, after her father, Thomas, was unable to attend for health reasons.
In her vows, Ms Markle will not promise to "obey" her husband and Prince Harry has chosen to have a wedding ring.
Prince Harry's ring will be a platinum band with a textured finish and Ms Markle's has been made from a piece of Welsh gold, Kensington Palace said.
Celebrity attendees include tennis star Serena Williams, TV personality James Corden, singer James Blunt, actor Carey Mulligan, and rugby star Jonny Wilkinson.
Prince Harry's uncle, Earl Spencer, the Duchess of York, Sarah Ferguson, and the Duchess of Cambridge's sister Pippa Middleton, are also at the service.
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