Allman died peacefully at his home in Savannah, Georgia, according to a statement posted on his website.
No cause of death was immediately given, but the statement said he had “struggled with many health issues over the past several years”.
Allman battled for years with heroin addiction and substance abuse and went into rehab several times before cleaning up in the 1990s.
The Allman Brothers Band’s music merged blues, jazz, country and rock with a meandering improvisational style that made jamming at concerts one of their trademarks.
Their best-known hits include Whipping Post, Midnight Rider, Melissa and Ramblin’ Man and their southern rock sound is credited with inspiring groups such as Lynyrd Skynyrd and the Marshall Tucker Band.
Allman’s older brother Duane, who co-founded the group, tragically died in a motorbike accident in 1971 at the age of 24, just as the band was enjoying its first big taste of success.
But Allman went on to front the band on his own for decades after his brother’s death.
He famously married singer and actress Cher in 1975, three days after she divorced Sonny Bono.
Their marriage was tumultuous from the start. Cher requested a divorce just nine days after their Las Vegas wedding, although she dismissed the suit a month later.
Together they released a widely-panned duets album under the name Allman And Woman. They had one child together, Elijah Blue, and Cher filed for legal separation in 1977.
Allman was inducted into the Rock & Roll Hall of Fame in 1995 and received a Grammy award for lifetime achievement in 2012.
His longtime manager and friend Michael Lehman was quoted in US media reports as saying: “I have lost a dear friend and the world has lost a brilliant pioneer in music.
“He was a kind and gentle soul with the best laugh I ever heard. His love for his family and bandmates was passionate as was the love he had for his extraordinary fans.”
Travis Tritt said on Twitter: “I’m so very saddened to hear of the passing of rock & blues legend Gregg Allman. He was such a huge influence on me.”
Keith Urban added: “My heart breaks today at the passing of soul brutha Gregg Allman. Blessings and peace to all the Allman family. – KU.”