The law, published Monday in the government’s online database, comes weeks after Putin had ordered the deal — signed in 2000 to allow both nuclear powers to dispose of plutonium from their defence programmes — be halted.
The Russian parliament had previously approved the legislation.
The move comes as Russia is locked in its worst standoff with the West since the Cold War over its 2014 annexation of Crimea, the conflict in Ukraine and stalled efforts to end the war in Syria.
In addition to tearing up the cooperation deal, Russia said earlier this month that it was suspending joint research on nuclear projects with the United States.
The law sets a series of unprecedented conditions for the deal to be reinstated, including the cancellation of Western sanctions against Moscow and the withdrawal of US troops from eastern European NATO members.