The royals are "establising themselves in their London home," Margareta Thorgren, the chief press officer for the Royal Court told the TT news agency on Tuesday afternoon, after Swedish tabloid Expressen broke the story.
O'Neill told the Expressen newspaper in July that Madeleine would soon be joining him in the UK capital, where he has been working since the spring after returning to Europe following a spell in New York.
“Madeleine and I have now taken the decision that we are going to stay in London in order for me to do my job,” he said.
He added that he had become tired of commuting, having spent much of this year travelling between New York, London and Stockholm.
“I do not want to come home to a hotel room by myself in the evening. I want to come home to my family and eat dinner together.”
Prince Nicolas pictured with his parents in July: Photo: Brigitte Grenfeldt/Swedish Royal Court
News of the couple's relocation emerged following another high profile royal announcement earlier in the day, when it was revealed that the christening of their son, Prince Nicolas, would take place at Drottningholm, the Swedish royal family's palace just outside Stockholm on October 11th.
Nicolas - who is the youngest member of the Swedish royal family - will be formally named Nicolas Paul Gustaf Bernadotte O'Neill.
One of the prince's middle names - Paul - honours Chris O'Neill's father Paul Cesario O'Neill, who died in 2004, while Gustaf is a name more commonly taken by members of the Swedish royal family. Bernadotte is the Swedish royals' family name.
Drottningholm is a 15th century palace with a place on UNESCO's World Heritage list. Some reports in the Swedish media had previously suggested that the baby would instead be christened in the Royal Palace in Gamla Stan, Stockholm's Old Town.
Prince Nicolas pictured in the week he was born: Photo: Swedish Royal Court
Princess Madeleine, 33, and Chris O'Neill, 41, have kept a low profile since the birth of Prince Nicolas, whose older sister Leonore is 18 months old.
Until recently, Madeleine has been living in a Stockholm apartment owned by the royal family.
Unlike her brother Prince Carl Philip, who works as a designer, she has not pursued her own career in Sweden, although she previously worked for the World Childhood Foundation in New York and regularly represents the royal family at formal events.
"I'm so thankful to be a mother of two. Both Leonore and her brother Nicolas are little angels," wrote the princess.
Princess Madeleine is expected to return regularly to Sweden, where she will continue to represent her family at charity events and on other official occasions.