The Eastern route will connect Russia's fields in eastern Siberia with northeast China through the city of Blagoveshchensk in the Russian Far East.
"Coordination and control of the implementation of the agreement are assigned to [Russia's] Ministry of Energy and the National Energy Administration of the People's Republic of China," the statement issued by the government's commission on lawmaking reads.
The bill is subject for further consideration by the government.
The Russia-China intergovernmental agreement was signed in Moscow on October 13, 2014, following Gazprom's $400-billion gas supply deal with CNPC (China National Petroleum Corporation), signed last May.
The Russian energy giant is set to export 38 billion cubic meters of Russian gas to China annually over a 30-year period.
The first supplies are scheduled for 2018 through the Power of Siberia pipeline, also known as the "eastern route". The construction of the pipeline began in September 2014.