In a Facebook post, guitarist Billy Gibbons and drummer Frank Beard said Hill died in his sleep at his home in Houston.
They did not give a cause of death, but a July 21 post on the band’s website said Hill was “on a short detour back to Texas, to address a hip issue”.
At that time, the band said its long-time guitar tech, Elwood Francis, would fill in on bass, slide guitar and harmonica.
Born Joe Michael Hill in Dallas, he teamed up with Gibbons and Beard to form ZZ Top in Houston in 1969.
The band released their first album, titled ZZ Top’s First Album, in 1970.
Three years later they scored breakthrough hit La Grange, which is an ode to the Chicken Ranch, a notorious brothel outside a Texas town by that name.
The band later had chart hits Tush in 1975, Sharp Dressed Man, Legs and Gimme All Your Lovin’ in 1983, and Rough Boy and Sleeping Bag in 1985.
The band’s 1976 Worldwide Texas Tour, with its Texas-shaped stage festooned with cactuses, snakes and longhorn cattle, was one of the decade’s most successful rock tours.
They were inducted into the Rock and Roll Hall of Fame in 2004.
Rolling Stones lead guitarist Keith Richards introduced the band to the Hall, saying: “These cats are steeped in the blues, so am I.
“These cats know their blues and they know how to dress it up. When I first saw them, I thought, ‘I hope these guys are not on the run, because that disguise is not going to work’.”
That look — with all three members wearing dark sunglasses and the two frontmen sporting long, wispy beards — became so famous as to be the subject of a New Yorker cartoon and a joke on The Simpsons.
This article originally appeared on HuffPost UK and has been updated.