Madonna said she is "overjoyed" to welcome her newly adopted twin daughters into her family.

Just 36 hours after a judge ruled she could legally adopt the twins, the music star boarded a private jet with her children as they left their birth country of Malawi to start their new life together.

The Like A Prayer singer, who had earlier denied reports that she was intending to adopt two children during a recent trip to the African country, went public with the happy news, sharing a picture on Instagram of herself walking hand-in-hand with the two girls named Stella and Esther.

In a statement she said she was grateful to those who made the process possible.

"I can officially confirm I have completed the process of adopting twin sisters from Malawi and am overjoyed that they are now part of our family," she said.

"I am deeply grateful to all those in Malawi who helped make this possible and I ask the media please to respect our privacy during this transitional time.

"Thank you also to my friends, family and my very large team for all your support and love!" she added.

The children, who have never been on a plane before, made the 18-hour journey to New York where the singer's other two adopted children, David and Mercy, who are also from Malawi, were waiting to meet their new siblings.

According to MailOnline the 58-year-old singer applied for custody of the girls at the High Court in the capital Lilongwe on 25 January.

The process began two years ago after Madonna filed paperwork to become their adoptive parent.

Court appointed guardian Dominic Misomali, 52, the Principal Social Welfare Officer for the Department of Gender, Children and Disability, said Madonna first met Stella and Esther at the Home of Hope Orphanage where she had adopted two previous children, David and Mercy.

"The application was lodged about two years ago. Madonna has followed the letter of the law and there have been no shortcuts. She has followed the correct procedure and that has taken the two years," Misomali said.

He added that the twin daughters were "very happy" and "very excited" about their new life.

Describing the moment the judge at the High Court in Lilongwe gave Madonna legal custody of the children, he told MailOnline: "You could see the motherly love from Madonna to the girls. They were so happy and Madonna was showing all her motherly instincts. She let one of the girls take off her glasses and put them on. They are very happy together.

"The children had lots of toys on the floor while the judge spoke and she let them play and not hush them up."

Misomali, who will travel to New York later this year to see how the girls are settling in, said as the singer held the girl's hands her maternal instinct was evident as they left together.

"They walked out either side of her and she was holding their hands. You could see the love she had for them in her face and she was already a mother to them. The girls are very happy and very excited about what is happening to them."

The twins were left to live in an orphanage after their natural mother died five days after giving birth due to complications from a caesarean section operation in August 2012. The girls' father, Adam Mwale, who has five other children including a grown up son, remarried and their grandmother had been unable to care for them.

The ruling said the twins' father gave his consent for the adoption and accepted it "permanently terminates" his parental rights – adding that he had not received any incentives.

Since adopting her children Mercy James and David Banda from Malawi, Madonna has forged a close connection with the country, raising $7.5m ($5.9m) for the construction of Paediatric Surgery Ward at Queen Elizabeth Central Hospital in Blantyre, which is scheduled to open early next year.

Acknowledging the singer's development projects in Malawi, judge Fiona Mwale (no relation to the girls' father) described her as "a good friend of the country".

"The court considered that since she is regularly coming into the country to visit these projects it means she will still be visiting the country therefore giving the children a chance to be closer to the family members," the judge observed.

Judge Mwale added that the singer would provide a loving family life for the children in "a luxurious, spacious and comfortable abode in an affluent neighbourhood" in the US.

"Her charity work brings her into contact with orphanages... and it was as a result of this contact that she felt compelled to fill a gap in their lives and open up her home to them," Mwale said. "The petitioner satisfied me that this adoption is motivated by her desire to offer a home, love, protection and guidance to the infants. She would like to share what she has with those who are less privileged."

It has since emerged that the Material Girl singer had posted photos of herself and her children Lourdes and Rocco with the twins on Instagram last summer.

The 58-year-old star wrote "3 Beauties!" next to the image of her daughter Lourdes cuddling the sisters on a visit to Home of Hope orphanage in July 2016.

Her other children Mercy and David have also met their new siblings on visits to Malawi.

Madonna, 58, adopted Malawian children David Banda and Mercy James in 2006 and 2009. The pop icon has two other children, Lourdes and Rocco, from previous relationships.

The children, who cannot speak English, will keep their original names of Stella and Esther as they begin a new life in the US.