Mr Snowden, who leaked classified information from the US National Security Agency, is now a fugitive in Russia.
Speaking to the BBC, Mr Snowden said the British spy agency, GCHQ, can access a personal smartphone by sending it an encrypted text message, and using it to take pictures and listen to conversations.
Mr Snowden said both the GCHQ and the US National Security Agency had invested in technology that allows them to hack smartphones.
Mr Snowden described in some detail the GCHQ's collection of secret intercept capabilities, known as the "Smurf Suit".
"Dreamy Smurf is the power management tool which means turning your phone on and off without you knowing," he said.
"Nosey Smurf is the 'hot mic' tool. For example, if it's in your pocket, GCHQ can turn the microphone on and listen to everything that's going on around you - even if your phone is switched off because they've got the other tools for turning it on."
"Tracker Smurf is a geo-location tool with allows GCHQ to follow you with a greater precision than you would get from the typical triangulations of cell phone towers."
Mr Snowden also explained that the SMS message sent by the agency to gain access to the phone would pass unnoticed by the handset's owner.
He said the encrypted text message used to access a phone can enter a person's phone without them noticing.
"It's called an 'exploit'," he said. "That's a specially crafted message that's texted to your number like any other text message, but when it arrives at your phone it's hidden from you. It doesn't display. You paid for it [the phone] but whoever controls the software owns the phone."
However, Mr Snowden said the NSA and GCHQ are not interested in tracking the average member of the public, rather these tools are used on those suspected of involvement in terrorism or other serious crimes such as paedophilia: "but to find out who those targets are they've got to collect mass data", he said.
