District and Sessions Judge Gyanaranjan Purohit at Cuttack, about 26 km from state capital Bhubaneswar, held Mitu Patnaik, Gajendra Digal and Saroj Badhai guilty, the nun's counsel Manas Ranjan Singh said.
The court would pronounce the quantum of sentence later in the day.
The 29-year-old nun was attacked by a mob and raped at Nuagaon village Aug 24, 2008, when communal violence in the region was at its peak.
The district, about 200 km from here, witnessed widespread violence after the murder of Vishwa Hindu Parishad leader Swami Laxmanananda Saraswati and four of his aides at his ashram. Police had blamed Maoists for the killings.
At least 38 people were killed in the state and thousands of Christians were forced to flee their homes.
The gang-rape had sparked an international outcry and drew strong condemnation.
The Crime Branch of the state police, which probed the case, arrested about two dozen people and filed four chargesheets.
In the first phase, the court tried nine accused and completed its hearing March 4 and had kept its verdict reserved.
While the court Friday convicted three people, it acquitted the remaining six due to lack of evidence.