The musician, who had recently taken leave from the band due to a hip problem, died in his sleep at his Texas home, a statement on the band’s Instagram confirmed.
Signed by Hill’s bandmates, Frank Beard and Billy Gibbons, it said: "We are saddened by the news today that our Compadre, Dusty Hill, has passed away in his sleep at home in Houston, TX.
"We, along with legions of ZZ Top fans around the world, will miss your steadfast presence, your good nature and enduring commitment to providing that monumental bottom to the 'Top'.
"We will forever be connected to that Blues Shuffle in C. You will be missed greatly, amigo. Frank & Billy."
Responding to the news, Mike Scott, lead singer of Scottish group the Waterboys, tweeted: “Rock in peace, Dusty Hill. 52 years together, the longest intact rock 'n' roll line-up in the world. Bandmates gonna miss him.”
ZZ Top had been booked to perform at a venue in Simpsonville, South Carolina, on Wednesday, but the show has now been cancelled, NBC reported.