"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."
Madeleine's brother and sister, Princess Victoria and Prince Carl Philip, also sent a message of congratulations, with Victoria saying that her daughter Estelle, who turns two-years-old later this month, was excited to meet the new addition to the family.
"We are all very excited that Madeleine and Christopher have become parents," read the siblings' statement. "We look forward to seeing the new family, especially Estelle, who is very curious about her new cousin. We wish them good luck!"
Princess Victoria with her daughter Estelle
Chris' mother, Eva-Maria O’Neill, revealed her excitement at meeting her new grandchild.
"I am very happy about my new granddaughter and I look forward to seeing her," she said. "I wish her all the best in life.
"I extend my warmest greetings to my son and Princess Madeleine and congratulate them on their first child."
Prince Carl Philip congratulated his sister
Christopher's sisters, Tatjana d'Abo and Countess Natascha von Abensperg und Traun, were equally overjoyed at the news.
"We are very excited about our new niece and relieved that everything has gone well," they said. "It is a long-awaited playmate to all the cousins. We know that our brother and Princess Madeleine will be wonderful parents and we wish them all the best."
The palace's statement added that anyone wishing to send messages of congratulations to the new parents could do so on the royal family and Princess Madeleine's Facebook page, where the news has already received more than 12,000 likes.
On Friday the royal household confirmed that Madeleine had given birth and said that "both mother and child are in good health."
"The Office of the Marshal of the Realm is delighted to announce that H.R.H. Princess Madeleine gave birth to a daughter on February 20, 2014 at 10.41 pm local time New York," the Swedish court announced.
Chris, who married his princess in a fairytale ceremony in June 2013, was reportedly present at the birth, which took place at New York Presbyterian Weill Cornell Medical Center.
In January the couple confirmed their decision to welcome the baby girl in New York rather than Madeleine's home country Sweden, as they have been living in the city for several years.
To celebrate the birth, there will be a firing of a 21-gun salute in Stockholm, as well as other locations across Sweden.