The 30-year-old Madeleine is the youngest of King Carl XVI Gustaf and Queen Silvia's three children and is fourth in line to the throne.
The tabloid Expressen reported early Thursday that O'Neill, a 38-year-old financier she met in New York, had proposed to the princess, and the couple confirmed the news in a brief video clip posted on the royal website.
"Chris proposed to me in New York at the start of October, and we are very happy," Madeleine said in the video, which was recorded Wednesday at the Drottningholm Palace outside Stockholm.
"Madeleine and I have known each other for two years and I recently summoned up the courage to ask her to marry me. Thankfully she said yes," O'Neill said in English with a British accent. He added a few words in Swedish, saying he was trying to learn the language "but it is difficult."
Madeleine said the wedding would take place in Sweden in the summer of 2013, and that more details would be released later.
Madeleine lives in New York where she works for the World Childhood Foundation, a nonprofit founded by her mother.
In 2010, she broke off an earlier engagement after media reports that her then-fiancÚ had cheated on her.
O'Neill was born in London and holds dual American and British citizenship, according to a CV released by the royal palace. He studied at a boarding school in St. Gallen, Switzerland, and holds a bachelor's degree in international relations from Boston University and a master's degree from Columbia Business School in New York.
O'Neill now works as a partner and head of research at Noster Capital, a hedge fund with offices in London and New York. His interests include Alpine skiing, tennis, golf, music, literature and Chelsea Football Club in London, the palace said.
Madeleine's elder sister, Crown Princess Victoria married her former fitness trainer Daniel Westling at a lavish ceremony in Stockholm in 2010. The couple had a baby, Princess Estelle, this year. O'Neill accompanied Madeleine to Estelle's baptism ceremony in May.
The Swedish royal family has only ceremonial duties, such as attending award ceremonies, promoting Swedish businesses abroad and supporting charities and foundations. As the head of state, the king also receives foreign dignitaries on formal visits to Sweden.
News of Princess Madeleine and O'Neill's engagement comes just days after another royal union was celebrated in Europe. Prince Guillaume of Luxembourg and Belgian Countess Stephanie de Lannoy were married Saturday in the tiny duchy's Notre Dame Cathedral.