Gen Videla was one of 30 members of the security forces charged with the murders.
Videla is already serving a life sentence for human rights abuses during his tenure.
During the trial, Gen Videla took responsibility for the army's actions during his rule.
The judges ruled that Gen Videla would have to serve his life sentence in a civilian prison.
Mr. Videla's later years would be dominated by a revolving door in and out of jail, house arrest and courthouses.
Mr. Videla was raised in the small rural town of Mercedes in Buenos Aires province, the son of an army colonel.
Maxima's father, Jorge Zorreguieta, had been Minister of Agriculture in the junta of General Jorge Videla, which terrorized Argentina in the 1980's.
Jorge Videla, to call in sick, so that he himself could preside over the Mass and intercede on behalf of the kidnapped priests.
Since then a number of high-profile figures from the regime have been convicted, including the de facto presidents Jorge Videla and Reynaldo Bignone.
BBC: Largest trial of 'Dirty War' crimes starts in Argentina
Mr. Videla served only five years before receiving a pardon by then-President Carlos Menem, part of a broad amnesty that Mr. Menem said would help heal wounds of the era.
The court said Gen Videla would be transferred to a civilian prison "immediately", while Gen Menendez would undergo medical tests to determine if he was fit to be transferred to a local prison.
And since June, Jorge Videla, a former junta leader, has again been detained (recently in his home) over the theft for adoption by military officers of babies born to prisoners (who were then murdered).
Gen Videla had been sentenced to life in prison for torture, murder and other crimes in 1985, but was pardoned in 1990 under an amnesty given by the president at the time, Carlos Menem.
The case of General Videla, who refused to testify before one federal judge last June about five kidnappings of which he is accused, has been folded into an investigation of more than 230 kidnappings by Adolfo Bagnasco, a judge known for keeping high-profile cases in the public spotlight.
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