"We happily announce a new restitution of identity," said the organization on its website.
Although the identity of the new grandchild has not been revealed yet, the human rights group said "the individual lives in Argentina outside the capital city of Buenos Aires.”
Estela de Carlotto, president of the organization said the grandmothers would hold a press conference Thursday, June 13 at which the grandchild will be present.
"We appreciate the displays of affection and happiness and we ask for your patience and prudence until Thursday, when we will be able to provide all the information about the case," the group added in a post on Twitter.
The organization is dedicated to searching for and restoring the identity of children who had been stolen from their legitimate families by agents of the military dictatorship and illegally given up for adoption to relatives or associates of the regime after their parents were killed by the soldiers.
The Grandmothers who formed their association in October 1977 have so far located and identified 129 children and estimate that around 500 children were kidnapped or born in detention during that era.
More than 300 people whose identities have been stolen and hidden during Argentina's last dictatorship have yet to be found.