His death came just over a year after he announced he had lung cancer and had to “call time” on the band and retire.
Keith Altham, his close friend and music publicist, said he had died at his home in Andover, Hampshire, surrounded by friends and family.
Altham announced the death of his "dear old pal" on his Facebook page, adding that the 1960s rock star had suffered a number of strokes recently.
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."
The band recorded an album with three members of REM and the success of the Wet Wet Wet version, which featured on the soundtrack of the hit film Four Weddings and a Funeral and spent 15 weeks at number one, allowed Presley to pursue his interest in crop circles and UFOs.
He published a book, Wild Things They Don't Tell Us, about the paranormal in 2002.