Hadijat Gatayeva and her husband, Malik, ran an orphanage in war-ravaged Chechnya that was featured in the 2005 Finnish documentary by Pirjo Honkasalo, which won 10 international film awards.
Gatayeva was also the subject of the 2008 book Angel of Grozny: Orphans of a Forgotten War by the Norwegian author Åsne Seierstad.
The couple later moved to Lithuania. There they were arrested in 2008 -- on charges that they and their supporters insist were trumped-up and politically motivated.
In 2009, they were convicted of child abuse by a court in Lithuania and sentenced to 10 months in prison.
After serving part of the sentence they were freed, whereupon they applied for political asylum in Finland.
They told Yle on Wednesday that they were delighted and greatly relieved by the decision.
"We're in shock with joy," Malik Gatayev said. "This is an extremely important moment in our lives."
The Finnish Immigration Service declined to comment, saying that it never issues public statements on individual cases.
Professor: Rare, but not unprecedented
A noted Finnish human rights expert, Professor of Public International Law Martin Scheinin, notes that it is extremely rare for political asylum to be granted based on an application from another EU member state, but that there are precedents. However he told Yle he cannot recall another case where Finland has granted such an application.