Gibson died Monday at Baptist Hospital, said Richard Frank, who is also a longtime friend of the Grand Ole Opry star.
Gibson's songs used plain language and riveting melodies to communicate strong emotions. He sang in a rich baritone and usually wrote about solitude and sadness involving love, earning him the nickname "the sad poet."
"Simple is the only way I can write," he once said.
Gibson was inducted into the Country Music Hall of Fame in 2001.
Born on April 3, 1928, Gibson was a poor boy from Shelby, N.C., who dropped out of school in second grade. But he became a songwriting genius who sold millions of records.
"The only thing I was any good at was music," he said in a 1997 interview.
Between 1958 and the mid-1960s, Gibson's records and his compositions, including "Sweet Dreams" and "Oh Lonesome Me," were hits for himself and many other performers.
"I Can't Stop Loving You" was recorded by more than 700 artists, but Ray Charles had the big pop version in 1962.
Gibson and others helped create the "Nashville Sound" in the 1960s - clean, uncluttered music that remains an influence today.
Somewhere along the way, the moody, shy kid from a sharecropping family began playing guitar. When a friend came home from Paris after World War II with records by the jazz guitarist Django Reinhardt, Gibson was captivated, and was experimenting with different styles by his mid-teens.
A friend helped him land a performing job with a Knoxville radio station. But things weren't what Gibson expected: The fans wanted old-time country, not Gibson's brand of crooning.
Gibson hung on to the radio job but struggled on $30 a week earned playing beer joints. One day after a radio show, Gibson started humming a melody and playing with words - not writing anything down at first, just seeing where the tune would lead.
It was the beginning of a classic - the haunting "Sweet Dreams," made famous by Patsy Cline in 1963.
On June 7, 1957, he wrote two of country music's greatest songs: "I Can't Stop Loving You" and "Oh Lonesome Me."
Gibson was living alone in a trailer outside Knoxville. A repo man had just picked up his vacuum cleaner and television when Gibson started strumming, exploring a swirl of words and melodies.
"When I wrote those two songs, I couldn't have been any closer to the bottom," Gibson once said.
"Oh Lonesome Me" was a hit again in 1990 by the Kentucky Headhunters.
Gibson's own recording fared modestly, but the song was a solid success for Faron Young as well as Cline. Gibson quit the beer joints and took up songwriting full time.
"Don's one of the most talented people I've known," the late Chet Atkins once said. Atkins produced Gibson's greatest hits. "I always name him when I talk about the most important people I've recorded."
By Joe Edwards