The 71-year-old was best known for the 1960s hit with the Troggs.
He died at his home in Andover, Hampshire, surrounded by his friends and family, his friend and music publicist Keith Altham said.
He announced the death of his "dear old pal" on his Facebook page, adding that the singer had recently suffered a number of strokes.
He said: "He was one very real person in a sometimes very unreal world.
"Our thoughts are with his wife, Brenda, and the family and those legion of fans who loved his music and his band. I will miss him hugely."
Presley founded The Troggs in the 1960s.
The band became famous with Wild Thing, and later With A Girl Like You and I Can't Control Myself.
Charlatans singer Tim Burgess hailed the Troggs frontman as a "true talent" and a "total one off."