Madonna has defended her intended adoption of a Malawian baby, saying she had acted "according to the law like anyone else who adopts a child".
TV footage showed a woman carrying a child through the airport
The singer said she wanted to "open up our home and help one child escape an extreme life of hardship, poverty and in many cases death".
Earlier the child, David Banda, was taken to the US singer's London home.
The one-year-old boy flew from Johannesburg overnight with a bodyguard and Madonna's personal assistant.
The baby arrived at London's Heathrow airport at 0630 BST, despite claims by some charities that the rules on adoption have been bent for the star.
Madonna said she and her husband Guy Ritchie began the adoption process months ago.
"This was not a decision or commitment that my family or I take lightly," she said.
She added her family would now take time "to experience the joy we feel to have David home".
Earlier, a statement from the star's publicist confirmed Madonna had been granted an interim adoption of the child.
The decision by a Malawian court gives the singer and her husband, film-maker Guy Ritchie, temporary custody of 13-month-old David Banda for 18 months.
A group of charities in Malawi had tried to stop the adoption, claiming it was unlawful because Madonna has not lived in the African country.
David was carried by the assistant through the airport, with a grey-hooded top hiding him from the view of surrounding press.
He was taken to the star's home near London's Marble Arch, where many of the world's media were waiting.
'No public circus'
He was reported to be remarkably alert following the long flight.
The couple's statement, issued on Monday evening, said the boy had been given a passport and visa.
Madonna's publicist Liz Rosenberg said the singer was "going to do her best to not make it a public circus".
During 18 months of temporary custody the couple "will be evaluated by the courts of Malawi per the tribal customs of the country," the statement said.
The baby was flown out of Malawi by private plane to South Africa on Monday, where the party boarded a scheduled flight for London.
The singer, 48, returned to the UK three days earlier, but David was unable to travel as he did not have a passport.
The Human Rights Consultative Committee of 67 Malawian organisations had been due to go to court on Monday seeking an injunction to halt the adoption process.
But it deferred the move, saying it wanted to interview an unidentified uncle of David's who was "said to be opposed to the adoption plan".
The committee insists that Malawian law prohibits international adoption and requires a minimum of 18 months' assessment.
But Penston Kilembe, director of child welfare in the Ministry of Gender, Child Welfare and Community Services, said Madonna and her husband had broken no laws.
"The process did not start today - Madonna's people have been pushing the papers for some time and her coming was just to sign the papers to conclude the process," he said.
The boy's father, Yohame Banda, has agreed to the adoption.
"What I want is a good life for my child," he said.