The 31-year-old gave birth on Thursday night in the US with the official announcement made by the Royal Court on Friday. Madeleine posted a picture of her daughter's footprint on father Chris O'Neil's forearm on her Facebook page with the words "I'm overwhelmed" which attracted over 20,000 likes.
Meanwhile, new father Chris O'Neill told reporters that the baby measured 50 centimetres in length and weighed in at 3.15 kilos, and added that he was also "overwhelmed."
"She looks just like her mother and has ten fingers and toes," said O'Neill who went on to state that the baby has brown eyes and brown hair.
The couple leaves hospital with their daughter on Saturday. Photo: Princess Madeleine of Sweden/Facebook
When quizzed by reporters how the delivery went the US citizen said there was no complications and that his wife was doing fine.
"It went very smoothly. I was there from the beginning to the end. She's a very strong woman."
O'Neill declined to elaborate on when the name of the new child will be announced, stating that he and his wife had discussed names but that he could not reveal anything yet.
News of the baby's arrival sparked a wave of congratulatory messages from the Swedish royal family and political establishment.
"Today is a day of great happiness and thankfulness. We are filled with great joy. We now hope that Princess Madeleine and Christopher will be able to enjoy this unique time with their young daughter in peace and quiet,"said King Carl XVI Gustaf and Queen Silvia.
Princess Madeleine's sister and fellow mother Crown Princess Victoria was equally thrilled with the news.
"We are all delighted that Madeleine and Christopher have become parents. We look forward to meeting the new little family, and Estelle in particular is very curious about her new cousin. We wish them every happiness!" she said in a joint statement with Prince Carl Philip.