The star, who is said to be "excited" at the news, was appealing against an earlier decision that she could not adopt Chifundo "Mercy" James, four.
In April, a judge ruled out the adoption saying prospective parents had to be resident in Malawi for 18 months.
But the appeals court said the star’s commitment to helping disadvantaged children had not been considered.
The singer has founded a charity, Raising Malawi, which helps feed, educate and provide medical care for some of Malawi’s one million-plus orphans.
The 50-year-old singer’s lawyer said he had called the singer after the ruling.
"It’s the wee hours of morning in New York but she is excited at the news," Alan Chinula said.
"As her lawyer I am happy that this has settled this contentious issue."
He said he was arranging a passport for Mercy and was waiting to hear from Madonna about travel plans for the child.