The 30-year-old princess, the youngest child of King Carl XVI Gustaf and Queen Silvia, met New York financier O'Neill while working in the United States with the World Childhood Foundation, a charity for marginalised children set up in 1999 by her mother.
The two will tie the knot in an afternoon ceremony at Stockholm's Royal Chapel before a horse and carriage procession through the city centre.
The 350-metre long royal cortege will take a shorter route than it did three years ago, focusing on the capital's medieval old town, Gamla Stan.
"Secondly, this is a private wedding -- the king is paying for it himself," he said.
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Still, thousands of people are expected to line the streets of central Stockholm to catch a glimpse of the newlyweds before they travel by boat from the island of Riddarholmen to a wedding banquet at Drottningholm Palace, where Princess Madeleine was born in 1982.
The Swedish capital will provide a picturesque backdrop with its 14 main islands and a Baltic Sea archipelago of some 24,000 islands.
"You will definitely notice that there's a royal wedding underway in Stockholm," Lundgren said.
Around 600 guests, including Crown Prince Fredrik of Denmark, Crown Prince Haakon of Norway and Princess Charlene of Monaco, have been invited to witness the exchange of vows. From Japan, Princess Takamado will be attending, while Britain is sending Prince Edward, Earl of Wessex.
Unlike Victoria, who is widely respected and admired for her easy-going and down-to-earth style, Madeleine has had a complicated relationship with the Swedish public.
In her early twenties, the tabloids dubbed her "the party princess" after she was photographed in nightclubs around Stockholm's trendy Stureplan square.
"Because she (rarely) gives interviews, we don't know her," he said.
"I think she's been punished by the media because she looks so good. The media like to put labels on her, and they're not always accurate," he added.
The perception of Madeleine as a carefree party girl became so widespread even ardent royalists began to worry.