The star has been granted the adoption order needed to take custody of the two four-year-old twin girls.
Just two weeks ago, the singer denied that she was involved in any adoption application in Malawi after news of her court case first emerged.
"I can confirm that Madonna has been granted an adoption order for two children," judicial spokesman Mlenga Mvula told AFP, adding they were twins called Esther and Stella.
Madonna, who set up a charity called Raising Malawi in the southern African nation in 2006, adopted Malawian children David Banda in 2006 and Mercy James in 2009.
Her publicist was not immediately available for comment on Tuesday.
On January 24, local media reports said the singer appeared before Justice Fiona Mwale, accompanied by two unidentified children and several other people, before being driven away in an SUV vehicle.
Later that day Madonna told US magazine People in a statement that "the rumours of an adoption process are untrue."
Madonna's charity is funding a surgical unit for children at the Queen Elizabeth hospital in Blantyre, the commercial hub of Malawi.