At the time she asked the media to "respect our privacy during this transitional time."
Madonna brought the case at London's High Court over a MailOnline article that caused her "considerable personal distress", her solicitor said.
The article revealed the girls' names, race, age, the fact they lived in an orphanage in Malawi and were the subject of pending applications for adoption by Madonna.
"The MailOnline published it at a time when, as the journalist ought to have appreciated, Madonna would be powerless to protect the girls from harm," solicitor Jenny Afia told Mrs Justice Nicola Davies on Thursday.
"Their actions could, in her view, have threatened the integrity and/or outcome of the adoption process which would have had potentially life-changing implications for the girls, as well as for Madonna and her family."
Ms Afia said Madonna would donate the damages to The Mercy James Institute for Paediatric Surgery in Malawi.
"She is pleased that at least some good can come out of the situation," Ms Afia said.
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