According to a press release from Sweden's Royal Court, the baby was born in Danderyd Hospital north of Stockholm at 13:45 on Monday afternoon.
“Both mother and child are doing well,” Svante Lindqvist, a spokesperson for the royal family, said in a statement.
Staff at Danderyd Hospital giving a press conference on Monday. Photo: TT
The young prince will be the sixth in line to the Swedish throne and is the second child of the Swedish princess and her British-born American financier husband Chris O'Neill. The couple's first child, Princess Leonore, was born in New York in 2014.
It has been an eventful few days for the Swedish royal family, with Prince Carl Philip marrying Sofia Hellqvist in a lavish ceremony on Saturday. The occasion was attended by his then heavily pregnant younger sister.
Tributes poured in following the new prince's birth, including from the country's prime minister Stefan Löfven.
“We rejoice with the parents and sister Leonore,” he said in a statement.
Global celebrity magazine Hello, the US Embassy in Sweden and UK-based royal watching site British Royals were among the first to tweet their congratulations in English.
Congratulations to Princess Madeleine and Christopher O'Neill on the birth of their baby son! – Sveriges Kungahus http://t.co/PcfZiBRU1H
— US Embassy in Sweden (@usembassysweden) June 15, 2015
— HELLO! (@hellomag) June 15, 2015
Congratulatons to Princess Madeleine of Sweden & husband Chris, who just welcomed their second child — a SON!
— British Royals (@britishroyals) June 15, 2015
Madeleine, 33, and her American husband, 40, were married in Stockholm on June 8th, 2013. The pair returned to Sweden from the US earlier this year but announced last month that they were planning to move to London after the new baby's birth.
“The whole family intends to move to England at some point in the autumn…The plan has always been that the family eventually would move on. Chris' business is mainly in England,” royal press spokesperson Margareta Thorgren told Swedish tabloid Aftonbladet, which broke the story.
O'Neill's mother Eve O'Neill lives in central London, while his sister Tatyana is based on an eighteenth century estate just outside the city.
The royal couple are currently living in an apartment owned by Sweden's royal family in central Stockholm.
READ ALSO: Prince Carl Philip marries Sofia Hellqvist