In a statement on the band's website, Presley, 70, said he had been diagnosed with the disease after he was taken ill at a gig in Germany in December.
"I am receiving chemotherapy treatment and at the moment not feeling too bad," Presley said.
"However I've had to call time on The Troggs and retire. I would like to take this opportunity to thank you all for the cards and calls and for your love, loyalty and support over the years."
Wild Thing, a cover of a song originally by the Wild Ones, propelled The Troggs, who hailed from Andover in southern England, to fame.
Amongst their other hits was "Love Is All Around," which was covered by Wet Wet Wet in 1994 for the British film "Four Weddings and a Funeral," achieving massive international success as a result.
According to media reports, Presley joked he would spend the royalties the song earned on investigating crop circles and UFOs, a phenomena with which he had become fascinated.
