Concluding the five-week trial, Judge Yasmin Barrios said she was "completely convinced" Rios Montt intended to eradicate the Ixil ethnic group, The New York Times reported Friday.
Barrios sentenced the 86-year-old general to 80 years in prison.
More than 100 witnesses, including military experts and Ixil survivors, had testified about how the general's forces killed their families and destroyed villages.
Jose Mauricio Rodriguez Sanchez, who had been Rios Montt's intelligence director, was acquitted of the same charges.
In testimony, Patrick Ball of the San Francisco-based Human Rights Data Analysis Group said 5.5 percent of the Mayan Ixil population was killed from April 1982 to July 1983.
In presenting her one-hour summary of the ruling, Barrios said Rios Montt, who was commander of chief of the country's armed forces, knew of the systematic killings of Ixil villagers and did nothing to stop them.
Rios Montt justified the killings by claiming the Ixil were leftist guerrillas.
His attorneys said they plan to appeal the conviction.
The conviction was the first of a former head of state by a national tribunal on charges of genocide, said Adama Dieng, a special adviser with the United Nations on the prevention of genocide.