He struck a plea bargain to qualify for a reduced sentence.
He was tried separately from five other men accused of the 2006 murder, which shocked human rights campaigners.
The court also ordered Lt Col Pavlyuchenkov to pay 3m rubles (£60,500; $97,500) in compensation to Politkovskaya's children.
The Politkovskaya family had demanded 10m rubles.
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