Crowds of flag-waving Swedes gathered outside the royal palace in Stockholm cheered as the newlyweds kissed three times before riding in a horse and carriage procession through the heart of the capital.
At the ceremony inside the royal chapel, O'Neill held back tears as his bride walked down the isle to a Swedish wedding hymn, minutes before Roxette singer Marie Fredriksson performed one of her best known Swedish ballads.
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The wedding, held in Swedish and English, was witnessed by other royals, including Princess Charlene of Monaco, Princess Takamado of Japan and Britain's Prince Edward, Earl of Wessex.
Other guests included Crown Prince Fredrik of Denmark, Crown Prince Haakon of Norway, fashion retailer H&M's chief executive Karl-Johan Persson and Duran Duran bassist John Taylor.
The bride, who turns 31 on Monday, wore a Valentino designed dress, made from pleated silk organza and ivory-coloured Chantilly lace, ending with a four-metre-long train.
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Her mother, Queen Silvia, wore a jade-coloured silk dress.
"Besides that breathtaking, all dominating feeling of love, love is also heartfelt sincerity, tenderness, and loving care. In Swedish we call it 'tillgivenhet' -- affection," said chief court chaplain Lars-Göran Lönnermark, who officiated the service.
With O'Neill's "I will" and Princess Madeleine's "Ja", the couple were pronounced husband and wife.
The photogenic princess met New York financier O'Neill while working in the United States with the World Childhood Foundation, a charity set up in 1999 by Queen Silvia. The engagement was announced in October last year.
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The 38-year-old groom has declined taking a royal title, which would require him to become a Swedish citizen and give up his job as a partner and head of research at Noster Capital, a previously relatively unknown hedge fund.
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The US-British businessman sparked controversy in November when he made an obscene gesture at a photographer, raising questions over whether he was a suitable spouse for the princess, who is fourth in line to the throne.
Unlike her sister Crown Princess Victoria who has charmed the Swedish people with her down-to-earth style, Madeleine has had an uneasy relationship with the public.
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In her early twenties, she earned a reputation for partying in Stockholm's trendy nightclubs. She has also appeared in the tabloids over her shopping sprees.
In 2003, the young royal was photographed driving on a pedestrian street.
Even in the run-up to her wedding, Madeleine made headlines for all the wrong reasons after being stopped by police for driving in the bus lane. The royal court has claimed the car had permission to do so.
Daniel Nyhlen, the author of a recently released book on Madeleine, noted that she "has a different style: you can hear that she's a member of high society."
"I think the wedding could mark the beginning of a calmer and more mature princess. You could say that the little sister has grown up," Nyhlen said.