She met the boy in an orphanage in 2006.
The pop star wasn't in court for Wednesday's ruling.
Madonna and her husband, Guy Ritchie, have been caring for the child, David Banda, in London. David turns 3 in November.
David's mother died when he was a month old. His father has said he believed he couldn't care for him alone, and that placing him in an orphanage was the best way to ensure David's survival. The father has said he didn't object to the adoption.
