The creation, which appeared in April, shows three 1950s-style secret agents, wearing brown trench coats and trilby hats, snooping on conversations in a telephone box.
It appeared overnight in the Gloucestershire town just a few miles from GCHQ, where the UK's surveillance network is based.
Residents saw a group of men packing away a large white tarpaulin in Fairview Road, before driving off in a maintenance van.
The celebrated "guerilla artist" from Bristol did not confirm he was behind the piece at the time but now he has claimed responsibility for it on his website.
On a link titled "Q&A", Banksy was asked four questions, including, "Did you paint the spies in Cheltenham?". He replied: "Yes."
Banksy was also asked about the best and worst things about street art, to which he answered: "Having to make your mistakes in public."
Another question was: "What's the deal with Sotheby's?"
Banksy replied: "As a kid I always dreamed of growing up to be a character in Robin Hood. I never realised I'd end up playing one of the gold coins."