“I am tired but very happy,” O'Neill told reporters on Tuesday morning. The dad-of-two smiled and gave a thumbs-up as he left Danderyd Hospital north of Stockholm just before 8am.
Madeleine gave birth to the couple's baby boy on Monday afternoon, just two days after her brother Prince Carl Philip married Sofia Hellqvist in a busy week for the royal family.
“They were overjoyed and there were tears of happiness. It was very beautiful,” head doctor Sophia Brismar Wendel told reporters at a press conference on Monday.
— Aftonbladet (@Aftonbladet) June 16, 2015
The new little prince was born at 13:45 according to a press statement by the Royal Court, weighing in at 49 centimetres and 3,080 gram.
He is sixth in line to the Swedish throne and is the second child of the Swedish princess and her British-born American financier husband O'Neill. The couple's first child, Princess Leonore, was born in New York in 2014.
READ MORE: Tributes pouring in for Sweden's royal baby
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.
Sweden's new prince is the third royal baby to be born in Sweden in three years. Victoria gave birth to Princess Estelle in 2012.
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.