The law enters into force on the day it is published.
The bill was passed by the Russian Lower House in May. The goal of the legislation is to defend Russia's sovereignty from "unfriendly actions" by Washington and other foreign states that have imposed political and economic sanctions on Moscow.
The law also allows for a temporary or definitive end to the cooperation with the countries or entities that have engaged in unfriendly actions toward Russia.
On April 6, Washington unveiled new sanctions on Russia over what it described as "global destabilization efforts." The sanctions list included senior government officials, and lawmakers, as well as major business owners and private and state-owned companies under their control.
The Russian Embassy in the United States said that the new package of sanctions is another hit to bilateral relations, adding that the sanctions will hurt thousands of Russian citizens who are part of the businesses that were targeted.