Mr Markle, 73, reportedly watched the ceremony from California. He told the US celebrity website, TMZ: “My baby looks beautiful and she looks very happy.”
Ms Markle’s mother, Doria Ragland, stayed with her daughter overnight before accompanying her to the chapel.
Dressed in a pale green Oscar de la Renta dress, with a neat hat, an emotional-looking Ms Ragland sat alone on the bride’s side of the chapel for some time.
As the witnesses were called to sign the register, Ms Ragland appeared to accept an outstretched hand from Prince Charles with some relief.
In her vows, Ms Markle did not promise to “obey” her husband, while the prince has broken with royal tradition by choosing to wear a wedding ring.
Prince Harry’s ring is a platinum band with a textured finish and Ms Markle’s has been made from a piece of Welsh gold.
‘Power in love’
The wedding service combined British tradition with modernity and the bride’s African-American heritage.
The Most Rev Bishop Michael Curry, the president of the US Episcopal Church, gave an address, the Rt Rev David Conner, Dean of Windsor, conducted the service and the Archbishop of Canterbury, the Most Rev Justin Welby, officiated.
“There’s power, power in love,” said Bishop Curry, who was invited to speak by Ms Markle.
“If you don’t believe me think about a time when you first fell in love. The whole world seemed to centre around you and your beloved.”
In a fiery, passionate speech, he also referenced the African-American spiritual song Down by the Riverside, which was sung by slaves, and when he realised he had gone on too long, he told his audience he had better wrap up as “we gotta get you all married!”
Speaking afterwards, Bishop Curry said it was “a joyful thing” to see diversity in the ceremony, adding: “That happened today, in different ways, different songs, different perspectives, different worlds and all of it came together and gave God thanks.”
Lady Jane Fellowes, the sister of Prince Harry’s late mother, Diana, Princess of Wales, gave a reading from the Song of Solomon.
Karen Gibson and The Kingdom Choir performed Ben E King’s soul classic Stand By Me during the service.
As the bride and groom signed the register, 19-year-old cellist Sheku Kanneh-Mason – who won the 2016 BBC’s Young Musician – performed three pieces by Faure, Schubert and Maria Theresia von Paradis.
He was accompanied by musicians from the BBC National Orchestra of Wales, the English Chamber Orchestra and the Philharmonia.
The gospel choir also performed Etta James’ uplifting version of Amen/This Little Light of Mine as the newlyweds left the chapel.
After the service, the duke and duchess travelled through Windsor along a route lined by tens of thousands of well-wishers.
The Royal Borough of Windsor and Maidenhead said more than 100,000 people visited the town on Saturday.
Analysis by BBC royal correspondent Jonny Dymond
It was a traditional wedding – the dress, the bridesmaids, the vows, the hymns. And it was very, very different.
The Palace made it clear in a stream of announcements that they wanted a different kind of wedding.
But it was the service that marked this out as a modern, diverse wedding for a modern, diverse couple: the Kingdom Gospel choir setting toes tapping, a young black cellist, and a breathtaking address from Bishop Curry, the President of the Episcopal Church.
Every royal wedding is a chance for the Royal Family to relaunch and reinvent. There may have been trouble in the week before the wedding. But that is in the past.
This wedding was about the future, a different future for the Royal Family.
The wedding cake is to be served at the Reception. It was designed by Claire Ptak and features elderflower syrup made at The Queen’s residence in Sandringham from the estate’s own elderflower trees, as well as a light sponge cake uniquely formulated for the couple. #royalweddingpic.twitter.com/kt5lE4tEn9
Guests were treated to a performance by Sir Elton John and were served langoustine canapes, Windsor lamb, and champagne and pistachio macaroons. Instead of a formal sit-down dinner, food was served in bowls.
The reception also included the cutting of the lemon and elderflower-flavoured wedding cake.
Guest Suhani Jalota, the founder of the India-based Myna Mahila charity, said Elton John performed a “mini-concert”. She added that speeches by the Prince of Wales and the groom were “lovely”, adding: “Some people were even crying.”
Posting on Instagram, David Beckham said: “Watching Harry as happy as he was makes us all proud of the man and person he has always been… what a day.”
Other celebrities attending were tennis star Serena Williams, TV personality James Corden, singer James Blunt, actress Carey Mulligan and former England rugby player Jonny Wilkinson.
Prince Harry’s uncle, Earl Spencer; the Duchess of York, Sarah Ferguson; and the Duchess of Cambridge’s sister, Pippa Middleton, were also invited.
Politicians, including Prime Minister Theresa May, were not invited, as it is not a state event.
But the former Prime Minister, Sir John Major – a special guardian on legal matters to Princes William and Harry after the death of their mother – was among the invited guests.