Read more: Russian senators pass 'foreign agent' media law, send to Vladimir Putin to sign
The new law can apply to anyone who distributes content that is produced by media outlets registered as foreign agents and receives payments from abroad.
Nine human rights groups, including Human Rights Watch and Amnesty International, had called for the legislation to be dropped as it was being approved by lawmakers.
Read more: Russia brands opposition leader Navalny anti-corruption group a 'foreign agent'
Russian opposition politician Alexei Navalny's organization has been labeled a foreign agent, as has the US-funded Radio Liberty/Radio Free Europe and Voice of America.