Once registered, they will face requirements now applied to foreign-funded non-governmental organisations.
US intelligence agencies allege that RT served as a Kremlin tool to meddle in the 2016 USA presidential election.
Russian President Vladimir Putin has harshly criticized the US demand regarding the RT as an attack on freedom of speech and warned that Russia would retaliate.
Russian Federation will be able to use the law "to give a timely retaliatory response", he said.
During the debates on Wednesday, the Duma speaker, Vyacheslav Volodin, called the bill a "symmetrical answer" to the USA and a signal "our media can't be treated like that".
The legislation, passed in retaliation for the registration of English-language Russian news network RT under similar legislation in the United States, was drafted hastily and will likely be signed into law by Russian President Vladimir Putin by the end of the month.
The Russian bill would allow the government to mirror the USA demands, said the chairman of the Duma committee for information, Leonid Levin.
The measure approved Wednesday does not specify which media outlets would be designated as foreign agents, or how the process would work.
"We are making it possible.to take selective retaliatory measures - that is the idea of the law, and I hope it will be enforced this way".
According to the draft legislation, media outlets designated as foreign agents would be subject to the same rules that now apply to foreign-funded non-governmental organizations.
Russian law adopted in November 2012 requires that all NGOs engaged in political activity and receiving foreign funding register as "foreign agents".
These media will have to declare full details of their funding, finances and staffing while all published materials, including on their websites and social media, must be marked as coming from a "foreign agent".
Critics of the law have said the definition of political activity is so loose that it could be used against nearly any non-governmental organisation.
Amnesty International has warned the law will allow the Russian authorities "to tighten their stranglehold on press freedom". Yahoo News has reported that the Federal Bureau of Investigation has interviewed a former Sputnik correspondent about his work at the website.
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Randolph County is in the process of expanding its site by rezoning 370 acres to add to the 1,500 acres that comprise the site. Out of all the states that were considered, only Alabama and North Carolina remain in the running.