The financial details of the tender were not disclosed.
With the tender, the project clears a hurdle before the owners, Russia's Novatek and France's Total, can take a final investment decision and for construction to get under way.
Questions over gas exporting rights, monopolised in Russia by Gazprom, are still holding back that decision, however. Novatek has long been lobbying for approval to ship gas from the project overseas.
Russia, the world's second biggest gas producer after the United States, exports the bulk of its gas to Europe via pipelines but needs to build LNG plants to gain other export markets, given that demand in Europe is weak.
Project operator Yamal LNG said on Monday the consortium was a successful bidder for engineering, procurement, supply, construction and commissioning of the facility, which would have an annual capacity of 16.5 million tonnes.
The project also entails the development of the South Tambey condensate and gas field in the Arctic area of the Yamal peninsula, which is expected to produce 15 million tonnes of LNG per year from 2018.
Russia currently has only one active LNG plant, which is operated by Gazprom, Royal Dutch Shell and Mitsui at Sakhalin-2 and produces around 10 million tonnes annually.