Snowden told the BBC's Panorama that GCHQ could gain access to a handset by sending it an encrypted text message and use it for such things as taking pictures and listening in.
Both the GCHQ and NSA have invested heavily in technology allowing them to hack smartphones, he added, saying the agencies "want to own your phone instead of you."
GCHQ controls phones using the agency’s "Smurf Suite," a collection of secret intercept capabilities individually named after the tiny blue cartoon characters.
"Dreamy Smurf is the power management tool which means turning your phone on and off with you knowing," Snowden 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 which allows [GCHQ] to follow you with a greater precision than you would get from the typical triangulation of cellphone towers."
Paronoid Smurf is a self-protection tool that's used to veil GCHQ's manipulation of your phone.
"For example," Snowden said, "if you wanted to take the phone in to get it serviced because you saw something strange going on or you suspected something was wrong, it makes it much more difficult for any technician to realize that anything's gone amiss."
Once GCHQ has gained control of the phone, Snowden said, the agency would be able to see "who you call, what you've texted, the things you've browsed, the list of your contacts, the places you've been, the wireless networks that your phone is associated with.
"And they can do much more. They can photograph you."
Snowden said the "exploit," the SMS message the agency sends to gain access to the phone, would pass unnoticed by the user.
"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 [the phone], but whoever controls the software owns the phone."
The NSA reportedly has a program similar to Smurf Suite.
The NSA and GCHQ are targeting suspected terrorist, Snowden said, "but to find out who those targets are they've got to collect mass data."
"They say, and in many cases this is true, that they're not going to read your email, for example, but they can and if they did you would never know," he said.