Privacy groups and some lawmakers accused GCHQ of the widespread illegal monitoring of electronic communications after Snowden, a former U.S. intelligence contractor, leaked documents in June last year disclosing details of its activities and those of its U.S. counterpart the National Security Agency (NSA).
In his final speech before stepping down as head of GCHQ, Iain Lobban said only a "miniscule" percentage of global emails, texts and images were stored, viewed or listened to.
"The people who work at GCHQ would sooner walk out the door than be involved in anything remotely resembling 'mass surveillance,'" Lobban said. "My staff are the embodiment of British values, not a threat to them."
Snowden's leaks, published in newspapers internationally, indicated that GCHQ and the NSA had intercepted and monitored phone, email and social media communications on a massive scale, causing global uproar.
Snowden fled the United States, where he faces charges, and has since been granted temporary asylum in Russia.
Civil liberties groups, parts of the media and some politicians have argued the disclosures about the scale of government monitoring showed it needed to be reined in and security agencies put under greater oversight.
Intelligence chiefs say the leaks have damaged operations, put lives at risk and allowed terrorists to change their methods of communication, making them harder to track.
"I want to make it absolutely clear that the core of my organisation's mission is the protection of liberty, not the erosion of it," said Lobban, who stands down on Friday after more than six years as GCHQ's director.
He said the agency's 6,000 employees, housed in a futuristic building in western England named the doughnut because of its shape, were committed to minimising intrusion into people's privacy, and would only do so, lawfully, in cases of national security or preventing or detecting serious crime.
The spies dissected internet information "with surgical precision" with only a small percentage of global communications being intercepted, he said. "Of that, we only store a miniscule percentage for a limited period of time.
"Of that, only a small percentage is ever viewed, or listened to, as permitted by our legal framework and self-evidently constrained by resource."
He said the checks on British spies were the most coherent in the world, and while he said they were "frustrated" when journalists disclosed details of their work or queried their integrity, that did not mean they resented a free press.
"It's crucial that the targets whose communications we seek to exploit for the purposes of our national security don't know what we can and can't do," said Lobban, who has worked for GCHQ for 31 years."Some things do need to remain secret. Secret does not have to equal sinister."