By Laura Smith-Spark, CNN

(CNN) -- And they're married! Britain's Prince Harry and US actress Meghan Markle sealed their wedding vows with a kiss on the steps outside Windsor's St. George's Chapel on Saturday, cheered on by delighted crowds.

The couple -- now the Duke and Duchess of Sussex -- then set off on a procession through the streets of Windsor in an open carriage drawn by four Windsor Grey horses.

The bridal party, including three-year-old Princess Charlotte, Harry's niece, waved enthusiastically as the couple departed from the chapel after a ceremony that was unprecedented in British royal history.

In a departure from tradition, Markle walked much of the way up the aisle unchaperoned, followed by her 10 bridesmaids and page boys -- a move that was seen as a powerful statement of her feminist principles.

Her elegant white dress with an open bateau neckline was by British designer Clare Waight Keller, Givenchy's first female artistic director. Her 16-foot-long veil was held in place by a diamond bandeau tiara lent to her by the Queen.

Only when she reached the 15th-century chapel's Quire was Markle accompanied for her final steps to the foot of the altar by Prince Charles, Harry's father.

Harry, flanked by his brother and best man Prince William, looked emotional as he waited at the altar, dressed in the frockcoat uniform of the Blues and Royals.

The couple sat with clasped hands as they listened to an impassioned sermon from Chicago-based bishop Michael Curry, the first African-American head of the Episcopal Church in the United States.

His fiery preaching style was a marked departure from the usually conservative tone of a British royal wedding. Harry could be seen saying "Wow" to Meghan as the sermon ended.

It was followed by a performance of the Ben E. King classic "Stand by me" by the Kingdom Choir, a group of 20 gospel singers.

Meghan was all smiles as she said her vows and gave Harry his wedding ring. The crowd could be faintly heard cheering outside as the couple were proclaimed husband and wife by the Archbishop of Canterbury, Justin Welby, the most senior cleric in the Church of England.

Big moments so far

• Harry's aunt Lady Jane Fellowes, the sister of his late mother, Princess Diana, gave the reading from the Book of Solomon.

• Palace revealed that Meghan's wedding ring has been made from Welsh gold and is a gift from the Queen, while Harry's is platinum.

• The Queen conferred the titles of Duke of Sussex, Earl of Dumbarton and Baron Kilkeel on Prince Harry, making Meghan the first-ever Duchess of Sussex.

The last to arrive before the bride was the Queen, wearing a lime silk dress, accompanied by Prince Philip.

Among the host of famous guests already waiting in the chapel were Oprah Winfrey, George and Amal Clooney -- dressed in an eye-catching yellow dress and hat -- tennis star Serena Williams, actor Idris Elba and singer James Blunt.

Former footballer and celebrity David Beckham stopped to hug a fan as he walked alongside wife Victoria Beckham, former Spice Girls singer turned fashion designer, toward the chapel door.

Guests connected to the royal family included Pippa Middleton and her parents and Tom Parker Bowles, who is the son of Prince Charles' wife, Camilla. Earl Charles Spencer -- brother of Harry's mother, the late Princess Diana -- was another of the guests, as was Harry's aunt Sarah Ferguson, the ex-wife of Prince Andrew.

Former Prime Minister John Major, who was made a guardian to William and Harry after Diana died in 1997, was another high profile guest. Current Prime Minister Theresa May was not invited.

Senior members of the royal family, Prince Charles, the Princess Royal, Prince Andrew and his daughters, Princesses Eugenie and Beatrice were among the last to arrive.

Crowds gathered in the streets of Windsor from early Saturday, hoping to catch a glimpse of the bride and groom as they process through the town in an open horse-drawn carriage following the ceremony. Other devoted royal fans have camped out for several days to get the best possible spot. Forecasters promise blue skies for the big day.

Many more people planned to rise early (or stay up all night) in the United States to watch as Harry, long a favorite with the British public for his irreverent good humor, tied the knot with his California-born bride.

The wedding represents a historic moment for the royal family, as it welcomes an outspoken biracial, American divorcée into its ranks.

In a reflection of its contemporary nature, the couple chose a modern set of wedding vows, with the text of the formal parts of the service taken from Common Worship, the Church of England's standard liturgy, first published in 2000. It is thought to be the first time that this text has been used in a royal wedding.

There was no promise by Markle to "obey" her husband. Rather, Meghan pledged to "love him, comfort him, honor and protect him." Harry has chosen to wear a wedding ring, unlike his brother.

The award-winning young cellist Sheku Kanneh-Mason was chosen to play during the signing of the register. The ceremony will end with the Etta James version of "Amen/This Little Light of Mine," a gospel song that became synonymous with the US civil rights movement.

The presence of Harry's mother was also felt at the ceremony. "Guide me o thou great redeemer" was sung at Diana's funeral, at her memorial service in 2007 and at Kate and William's wedding in 2011.

Guests from Markle's side included cast members from "Suits" -- the legal drama in which she made her name. Actresses Abigail Spencer, Sarah Rafferty, Gina Torres and actor Gabriel Macht were all seen arriving.

It appeared that TV legend and philanthropist Winfrey, dressed in Stella McCartney with a large hat, would be seated in the Quire with the family and other close friends, rather than in the main body of guests in the nave.

In an effort to be inclusive, the couple invited 2,640 members of the public, including 1,200 ordinary people from communities around the United Kingdom, to watch from inside the castle grounds as the guests arrived.

Among them were Helen McKenzie and Louis Davidson, who were invited through their local community in Somerset. "We got the invitation a while ago but had to keep it secret. It wasn't easy!" Davidson told CNN as the pair headed into the castle.