He died on Tuesday in Nashville at an Alzheimer’s facility surrounded by his family, his publicist says.
Campbell announced in 2011 he was suffering from dementia before embarking on a US-wide farewell tour.
He began his career as a well-regarded recording session guitarist in Los Angeles before becoming a fixture on the US music charts, radio and television in the 1960s and ’70s.
He won six Grammy Awards and had nine No.1 songs in a career of more than 50 years.
Campbell released a final studio album in June, Adios, which was recorded after his farewell tour ended in 2012.
His death brought tributes from country music stars.
Singer Brad Paisley thanked Campbell on Twitter “for the artistry, grace & class you brought to country music. You were a shining light in so many ways”.
Dolly Parton released a short tribute video and tweeted he “was one of the greatest voices of all time. I will always love you, Glen!”
Glen Campbell was one of the greatest voices of all time. I will always love you, Glen! pic.twitter.com/LQFEWA42lF
— Dolly Parton (@DollyParton) August 8, 2017
Campbell was one of 12 children of Arkansas sharecroppers and began playing guitar at age four.
After a teenage marriage and divorce, he married again and headed to Los Angeles in the late 1950s.
Campbell became part of The Wrecking Crew, a group of sought-after session players who recorded with Elvis Presley, Frank Sinatra, Dean Martin, the Monkees and Nat King Cole.
He also became a touring member of The Beach Boys, filling in for Brian Wilson, who did not like to go on the road.
Campbell had a breakthrough solo hit with “Gentle on My Mind” in 1967, quickly followed by “By the Time I Get to Phoenix” and “Wichita Lineman”.
He starred opposite John Wayne in the 1969 film True Grit and earned an Oscar nomination for singing the movie’s theme song.
Campbell was among a wave of country crossover stars that included Johnny Cash, Roy Clark and Kenny Rogers, and like many of his contemporaries he enjoyed success on television, beginning a three-year run with The Glen Campbell Goodtime Hour in 1969.
His later hits included “Galveston”, “Dreams of the Everyday Housewife” and, in 1975, the chart-topping pop-crossover song “Rhinestone Cowboy”.
Written and recorded by Larry Weiss in 1974, the song received little attention until Campbell heard it on the radio and quickly related to the story of a veteran performer who triumphs over despair and hardship.
As he would confide in painful detail, Campbell suffered for his fame and made others suffer as well.
He drank heavily, used drugs and had a turbulent relationship with country singer Tanya Tucker in the early 1980s.
He is survived by his wife, Kim; their three children, Cal, Shannon and Ashley; and his children from his three previous marriages, Debby, Kelli, Travis, Kane and Dillon.