CMT News confirmed the musician's Thursday death, but did not report a cause of death.
Funeral arrangements had not been announced as of Friday.
The Tennessee native learned to play guitar when he was 8 and appeared in local talent shows before performing live on local radio while he was still in his teens, CMT said.
As an adult, Greene performed with the Cherokee Trio, the Rhythm Ranch Boys, Cecil Griffith & the Young 'Uns and the Texas Troubadours. He also enjoyed a successful solo career.
He was inducted into the Grand Ole Opry in 1967 and remained a member until his death, CMT said.
Among his hits are "All the Time," "You Are My Treasure," "I Need Somebody Bad," "Until My Dreams Come True," "Yours for the Taking," "If It's Love [Then Bet It All]" and "Statue of a Fool."
Greene and singer Jeannie Seely recorded the popular song, "Wish I Didn't Have to Miss You."