Madonna spoke of her joy at bringing an African baby boy home to Britain and defended her adoption of him.
The singer said she and husband Guy Ritchie began the adoption process many months ago and had acted "according to the law like anyone else who adopts a child".
The couple chose 13-month-old Malawian boy David Banda after learning there were more than one million orphans in the impoverished country.
She said yesterday that it was her wish "to open up our home and help one child escape an extreme life of hardship, poverty and in many cases death", adding: "This was not a decision or commitment that my family or I take lightly."
The family will now take time "to experience the joy we feel to have David home".
The superstar has sparked anger among children's charities and human rights groups who claim she has used her celebrity to "buy" a baby and bypass the normal procedures.
But in an open letter, Madonna insisted: "After learning that there were over one million orphans in Malawi, it was my wish to open up our home and help one child escape an extreme life of hardship, poverty and in many cases death, as well as expand our family.
"Nevertheless, we have gone about the adoption procedure according to the law like anyone else who adopts a child. Reports to the contrary are totally inaccurate."
The family will undergo an 18-month evaluation as David's temporary custodians "after which time we hope to make this adoption permanent", she said.
David arrived in Britain yesterday to start his new life with one of the world's biggest stars.
Cradled in the arms of Madonna's personal assistant and accompanied by a bodyguard, he was driven from Heathrow airport to the singer's luxury London home.
A huge throng of photographers, reporters and film crews from across the world greeted his arrival at the mansion near Marble Arch.
His privileged new life is a million miles from the poverty of the orphanage in Malawi where he was placed by his father after his mother died.
Madonna and Ritchie have secured an 18-month temporary custody order from the Malawi courts.
It is thought the baby arrived in the UK with a US visa stamped in his new passport, sparking speculation that he would be adopted under US law.
Westminster Council, which covers the area where Madonna lives, said they "regularly" received applications from residents wishing to adopt from overseas.
But a spokesman could not confirm if they had received any such application from the singer.
Adoption experts said the celebrity couple would have undergone rigorous checks before being given permission to adopt the boy.
But British adoption agencies and aid organisations said adopting individual children from overseas was not the answer for the hundreds of thousands suffering from deprivation.
Anna Feuchtwang, from EveryChild, said: "Most evidence shows that children are better off in their own families and communities."
Louise Richards, from War on Want, added: "Madonna's step to adopt the baby is a well-meaning, but misguided act."
There has also been a backlash in Malawi, with human rights groups going to court to question the apparently speedy decision about David's future.
In the capital Lilongwe, it was claimed that the courts had improperly waived Malawian laws to allow Madonna and Ritchie custody because of their celebrity status.
Justin Dzonzi, a lawyer for a coalition of human rights and child advocacy organisations, said his group was asking a judge to review the adoption.
Other organisations said they wanted to ensure child protection regulations were not swept aside to benefit a singer who has been generous to Malawi.
Two months ago the pop superstar announced she was to donate three million dollars (£1.6 million) to the country through the Raising Malawi charity.
The furore began last week with pictures of Madonna and Ritchie visiting orphanages in Malawi and the news that they had been given temporary custody of David.
Her spokeswoman Liz Rosenberg said: "The interim adoption grants David's new parents temporary custody for 18 months, during which time they will be evaluated by the courts of Malawi per the tribal customs of the country."
They left Malawi last Friday. David was put on a private jet from Malawi to South Africa and then took an overnight flight from Johannesburg on Monday.
Malawi law requires that would-be parents live in the country for a year while social welfare officers investigate their ability to care for the child.
The court order waived such a stipulation but said David must be returned to Malawi if Madonna was seen to be treating him differently from her other children, Lourdes, 9, and Rocco, 5.