"At 10:41 last night we brought a little girl into this world," said 39-year-old Chris in a press conference on Friday. "She looks like her mum which is all I wanted."
"We have ten fingers, ten toes," he added. "And she's got a very strong, nice roar on her."
"She weighs 3150 grams and measured 50 centimetres," added Sona Degann, a gynaecology specialist at New York Presbyterian Hospital. "And she is beautiful and healthy."
"I do have a footprint here from her last night," said Chris, showing off an inked footprint on his forearm, which featured in a photograph posted by the Swedish royal family's official Facebook page on Friday evening.
"He [Chris] was at her side at all times," said Sona. "Made her comfortable and most importantly - happy."
"The princess handled it wonderfully," Chris stated of 31-year-old Madeleine, whom he married in June 2013. "She's a very strong woman and she's resting now obviously as I would try to do afterwards, we haven't had much sleep."
"Her eyes are dark brown right now," he added of his daughter, who is yet to be named. "And her hair is also dark brown right now, but that changes all the time with babies."
While Chris, Madeleine and their new arrival were enjoying their first days as a family, the royal birth was being celebrated across the princess' native country.
A 21-gun salute was fired in Stockholm, where the couple tied the knot last year, as well as other locations across Sweden.
The new parents' families also excitedly released statements of congratulations to Madeleine and Chris.
"We know today both happiness and warm thanks," said King Carl XVI Gustaf and Queen Silvia. "Our joy is great. We wish now that Princess Madeleine and Christopher get peace and quiet and can take advantage of this unique time with her little daughter."
"We are all very excited that Madeleine and Christopher have become parents," added the new mum's sister, Princess Victoria. "We look forward to seeing the new family, especially Estelle, who is very curious about her new cousin. We wish them good luck!"
"I am very happy about my new granddaughter and I look forward to seeing her," said Chris's mother Eva-Maria O'Neill. "I wish her all the best in life."