Martha E. Moore, his publicist, said Cochran died Thursday morning at his home in Hendersonville north of Nashville.
He had been in declining health in recent years, and suffered an aortic aneurysm in March. He was diagnosed with pancreatic cancer two years ago.
He also wrote the No. 1 hits: "Don't You Ever Get Tired of Hurting Me" by Ronnie Milsap; "He's Got You" by Cline and Loretta Lynn; "I Want to Go With You" by Arnold; and "That's All That Matters to Me" by Mickey Gilley.
This pleading sentiment was expressed in 1965 in "Make the World Go Away":
"Make the world go away.
"And get it off my shoulders.
"Say the things you used to say
"And make the world go away."
Survivors include his wife, three sons and a daughter. A private memorial service will be held later. His ex-wife is Grand Ole Opry singer Jeannie Seely.
Cochran was born in Isola, Miss., and worked the New Mexico oilfields as a young man. He was a member of the Nashville Songwriters Association International Hall of Fame and the Mississippi Musicians Hall of Fame.