Under bright spring sunshine, framed by white English flowers, the newlyweds paused and kissed to the cheers of the 1200 guests who had been invited to watch them leave.

Just minutes earlier, the Archbishop of Canterbury, Justin Welby, declared the couple husband and wife.

Their glittering union brings a measure of modern Hollywood glamour into the monarchy, reflected in a ceremony that combined modernity and the ancient rituals of a royal house that traces its line back to 1066.

Markle entered the chapel unescorted, dressed in a flowing white wedding gown created by British designer Clare Waight Keller and wearing a veil and diamond tiara.

Prince Charles, heir to the throne and Harry's father, accompanied Markle to the altar from the middle of the chapel, with her father too ill to attend.

Harry, looking nervous, appeared to say: "Thanks Pa" to Charles and "You look amazing!" to his beaming bride.

Markle's mother, Doria Ragland, 61, - who traveled with her to the chapel - shed tears as she sat alone across from the royal family. A gospel choir sang American soul singer Ben E. King's 1960s hit "Stand by me".

"There's power in love," black US bishop Michael Bruce Curry told a congregation that included Queen Elizabeth, senior royals and celebrities such as US mogul Oprah Winfrey, singer Elton John, David Beckham and George Clooney.

"Do not underestimate it. Anyone who has ever fallen in love knows what I mean," Curry told the congregation in an energetic, passionate address that quoted US 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.

Alongside tradition, there was innovation, by British royal standards. Markle, 36, who has been married before, did not vow to obey her husband; Harry, three years her junior, will wear a wedding ring - unlike other senior male royals.

The couple kissed on the steps of St George's Chapel before climbing into a 19th-century open horse-drawn coach for a tour of Windsor, where tens of thousands of cheering well-wishers crammed the streets to catch a glimpse of the newlyweds.

The world's media have been gripped by the occasion, and television channels beamed the ceremony across the world.

In Windsor, 20km west of London, tens of thousands of fans lined the Long Walk promenade leading to the castle, waving British flags and cheering.

Air traffic controllers for the nearby Heathrow Airport, one of the world's busiest, closed the airspace over the town for the 15 minutes before the ceremony.

The chapel was garlanded 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 Windsor's narrow roads.

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 was still present in the order of service.

After watching the ceremony from California, he told TMZ it had been "emotional and joyful":

"My baby looks beautiful and she looks very happy. I wish I were there and I wish them all my love and all happiness."

The service was conducted by the Dean of Windsor with 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.

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.

Australian Associated Press