Chris O'Neill, who has dual American-British citizenship, made the remarks about the wedding on Saturday to Norwegian broadcaster TV2, which caught up with him on a street in central Stockholm.
Princess Madeleine and O'Neill had just attended a national day ceremony along with King Carl Gustaf, Queen Silvia and other members of the royal family at the Skansen open air museum in Stockholm.
In his speech, the king said he was glad to see his daughter Madeleine "had found love and someone to build a future with."
On Friday evening, the king and queen will host a private dinner for the couple and their guests at the Grand Hotel, located on the Stockholm waterfront opposite the Royal Palace.
After Saturday's wedding ceremony at the Royal Chapel in Stockholm, the newlyweds will travel by carriage to nearby Riddarholmen, where they and their guests will board steamboats which will ferry them to Drottningholm Palace just outside Stockholm for the banquet.
Guests include the crown princes of Denmark and Norway, Britain's Prince Edward and Japan's Princess Takamado.
Princess Madeleine chose a wedding dress from Italian couturier Valentino, unlike her sister Victoria who opted for a Swedish designer for her nuptials to her former personal trainer in 2010.
A modern love story
Madeleine (30) the youngest of King Carl Gustaf and Queen Silvia's three children and fourth in line to the throne, was born at the palace.
She met her millionaire financier husband O'Neill (38) through mutual friends in New York, where Madeleine moved after she broke off a previous engagement to a Swedish lawyer in 2010.
She works for the World Childhood Foundation (WCF), a charity set up by her mother. The couple plan to continue to live in the city.
The thoroughly modern couple chose to announce their engagement in October via the royal family's website, accompanied by an intimate black and white picture taken by celebrity French photographer Patrick Demarchelier.
O'Neill is to continue his work as a banker and will not be given a royal title, the palace has said. – Sapa