The document confirms that his application for asylum in Russia is being considered but allows Snowden to cross the Russian border so long as border guards do not object, RIA Novosti news agency said.
The agency added that the document was initially given to the lawyer helping him, Anatoly Kucherena, who was now on his way to Sheremetyevo airport and about to arrive.
"The American is currently getting ready to leave. He is being provided with new clothes," Interfax said.
RIA Novosti cited a source within the Russian border guards service as saying he would be allowed to leave the airport as soon as he presents the document.
Snowden earlier this month applied for asylum, a process that could take up to three months. Kucherena has said he may even apply for Russian citizenship.
