The newspaper said Mr Snowden would be able to challenge the US request for his extradition in court in Hong Kong, where he is understood to be hiding.
The charges are said to have been filed by federal prosecutors in the Eastern District of Virginia, whose jurisdiction includes the main base of Mr Snowden's former employer, Booz Allen Hamilton.
The Post report said the US Justice Department had declined to comment on the claims.
The US has asked Hong Kong to detain National Security Agency whistleblower Edward Snowden on a provisional arrest warrant after charging him with espionage, The Washington Post has reported, citing American officials.
The intelligence gathered by GCHQ - after the intelligence agency allegedly accessed fibre-optic cables - is understood to have contributed to a number of arrests and convictions including a terror cell in the Midlands who were jailed for planning co-ordinated attacks.
It is also claimed to have led to the arrest of five Luton-based individuals preparing acts of terror, and three London-based people planning attacks prior to the Olympics.
A source with knowledge of the work of the intelligence agencies told the Press Association: "It's not about going through everybody's emails or phone calls. It's about homing in on criminal activity in order to lead the intelligence agencies to be able to take action."
The source added that the vast majority of the data gathered was discarded, with the agency focused on the "needles" of relevant information within the "haystack" of material.
– GCHQ spokesperson
We do not comment on intelligence matters. Our intelligence agencies continue to adhere to a rigorous legal compliance regime. GCHQ are scrupulous in their legal compliance.
"It's not just a US problem. The UK has a huge dog in this fight," he said. "They (GCHQ) are worse than the US."
The information is the latest leak from Mr Snowden, who has been responsible for a string of disclosures about US intelligence operations.
British intelligence agency GCHQ secretly accessed fibre-optic cables carrying huge amounts of internet and communications data, according to documents released by National Security Agency (NSA) whistleblower Edward Snowden.
The agency is able to tap into and store data from the cables for up to 30 days so it can be analysed under an operation codenamed Tempora, The Guardian reported.
GCHQ would not comment on intelligence matters but insisted it was "scrupulous" in complying with the law.
The newspaper said there were two principal components to the agency's surveillance programme, called Mastering the Internet and Global Telecoms Exploitation.
It claimed the data was shared with the organisation's US counterpart the National Security Agency (NSA).
The information is the latest leak from Mr Snowden, the whistleblower responsible for a string of disclosures about US intelligence operations.