Markle entered the chapel unescorted, dressed in a flowing white gown created by British designer Clare Waight Keller and wearing a veil and diamond tiara.
In a ceremony that combined modernity and the ancient rituals of a royal house that dates back to 1066, Prince Charles, heir to the throne and Harry’s father, accompanied Markle to the altar from the middle of the chapel.
Harry, looking nervous, appeared to say: "Thanks, Pa" to Charles and "You look amazing!" to his bride. Markle’s mother, Doria Ragland, 61, shed tears. A gospel choir sang American soul singer Ben E. King’s 1960s hit "Stand by me".
"There’s power in love," black U.S. bishop Michael Bruce Curry told a congregation that included Queen Elizabeth, senior royals and celebrities such as U.S. mogul Oprah Winfrey, singer Elton John and former soccer star David Beckham.
"Do not underestimate it. Anyone who has ever fallen in love knows what I mean," Curry told the congregation in a powerful, energetic address that quoted U.S. civil rights campaigner Martin Luther King.
The newlyweds will be known as the Duke and Duchess of Sussex, putting them in the senior ranks of British royalty.
But alongside tradition, there was innovation, by British royal standards. Markle, 36, did not vow to obey her husband; Harry, three years her junior, will wear a wedding ring - unlike other senior male royals.
The world's media have been gripped by the occasion, and television channels beamed the ceremony across the world.
To some Britons, the wedding of a senior member of the royal family to a divorcee whose mother is African-American and father is white embodied a modern Britain where race or background are no bar to even the most elite and traditional of institutions.
To others, it was an irrelevance or mild distraction from the schism of Brexit, which has deeply divided the United Kingdom; polls suggested that most Britons would not bother tuning in.
But in Windsor, tens of thousands of fans lined the Long Walk promenade leading to the castle, waving British flags and cheering as Markle's Rolls-Royce limousine drove past.
Air traffic controllers for the nearby Heathrow Airport, one of the world's busiest, closed the airspace over Windsor for the 15 minutes before the ceremony.
Hours before, Elizabeth had bestowed the title of Duke of Sussex on her grandson, a step that meant the actress, star of the TV drama "Suits", became a duchess when she married Harry.
SUNSHINE AND BEARSKINS
Under clear skies and glorious sunshine, a military band in scarlet uniforms and bearskin hats entertained excited fans gathered behind barriers. Police armed with semi-automatic rifles patrolling streets and watching from rooftops.
Among celebrity guests, American actor George Clooney and his wife Amal were joined by Beckham, his fashion designer wife Victoria and James Corden, British host of the American TV chat show "The Late Late Show".
Other guests included tennis ace Serena Williams, the siblings of Harry's late mother Princess Diana, Elton John, who sang at Diana's 1997 funeral, British actor Idris Elba, and two of Harry's ex-girlfriends.
The chapel was adorned with white roses, Diana's favourite flowers.
"This is a moment when we can all celebrate the rebirth of the royal family," said Kenny McKinlay, 60, who had come down from Scotland for the wedding. "It's a time when all the nation can come together rather than being divided. It's a day when you can be proud to be British."
The royal couple, who met on a blind date in 2016 and fell in love in a tent under the stars in Botswana, tied the knot in a castle that has been home to 39 English monarchs since 1066.
With security tight, tens of thousands of visitors had to pass through police search points set up around the castle to cram into the narrow roads of Windsor, about 20 miles (30 km) west of London.
FATHER NOT PRESENT
Markle's own father Thomas Markle, 73, a former lighting director for TV soaps and sitcoms, pulled out of the ceremony this week, telling the U.S. celebrity website TMZ he had had heart surgery on Wednesday.
Confusion over his attendance marred the build-up to the wedding, which had been choreographed for months by royal aides, and his name still appears in the order of service.
The service was conducted by the Dean of Windsor with Justin Welby, Archbishop of Canterbury and spiritual head of the Anglican Church, overseeing the exchange of vows.
Lady Jane Fellowes, Diana's sister, delivered the reading.
After the ceremony, the newlyweds are expected to greet some of the 1,200 members of the public invited into the castle grounds before starting a carriage procession through Windsor.
A reception will be held in the castle's St George's Hall before 200 guests join the couple at an evening event at the nearby Frogmore House mansion.
Harry and Meghan will carry out their first official engagement as husband and wife next week.
The British remain broadly supportive of the monarchy, albeit with a sense of mild irony about the pomp and pageantry that accompanies it, though most have deep respect for Queen Elizabeth after her 66 years of service as head of state.
Harry, along with brother William and his wife Kate, are at the forefront of efforts to modernise the monarchy by talking openly about their feelings.
"It is patently obvious - the more you say, the more you can be examined," said royal historian Hugo Vickers. "Everything moves on gradually - but there are certain risks, and there is a lot to be said for maintaining the mystique."
