The joint venture will make a range of Volkswagen brands including the Jetta, Skoda Octavia and Skoda Yeti models, the sources said.
The Russian press departments of both firms declined to comment on the matter.
Volkswagen had said in October that it was in advanced talks on manufacturing vehicles together with GAZ.
Foreign carmakers have stepped up efforts to form partnerships with local Russian firms to increase production, which then allows them to take advantage of government incentives and meet growing demand as the Russian market revives.
The Boston Consulting Group said this week that Russia would be the sixth-largest global auto market by 2020, with annual sales of 4 million units, up from its current 10th position.
Russia will overtake Germany by 2018 as the largest producer of passenger cars and light commercial vehicles in Europe, the consultancy said.
A number of multinationals, including Ford, VW, GM and Toyota already produce cars in Russia, but a local partner helps firms to reach a 300,000 unit annual minimum required to qualify for a range of incentives.
The government reduces customs duties on parts for firms that meet this minimum annual output level and also localize a larger portion of the manufacturing process.
GAZ, controlled by industrial tycoon Oleg Deripaska, will use its plant in Nizhny Novgorod for the joint-venture project. It has an annual capacity of 120,000 units per year.
VW will use its Kaluga facility in Russia, where its 150,000 unit capacity can be expanded to produce 180,000 vehicles per year.