A Facebook statement said he died in New York City from complications arising from rheumatoid arthritis, colitis and pneumonia.
“It is with the heaviest of hearts that we announce the passing of our comrade, Eagles founder, Glenn Frey, in New York City on Monday, January 18th, 2016.
“Glenn fought a courageous battle for the past several weeks but, sadly, succumbed to complications from Rheumatoid Arthritis, Acute Ulcerative Colitis and Pneumonia.
“The Frey family would like to thank everyone who joined Glenn to fight this fight and hoped and prayed for his recovery.
“Words can neither describe our sorrow, nor our love and respect for all that he has given to us, his family, the music community and millions of fans worldwide.”
The Eagles was one of the most successful bands of the 1970s, with multiple hit singles including Hotel California, in 1976.
Glenn co-wrote Hotel California with singer Don Henley. He wrote a number of the band’s biggest songs on his own, including Heartache Tonight and Lyin’ Eyes.
Glenn also got into acting, snagging a recurring role on Miami Vice.
He reunited with The Eagles in 1994 for their monster Hell Freezes Over tour and recorded music till the end, releasing what would be his fifth and final solo LP, After Hours, in 2012.
The Rock and Roll Hall of Famer had been fighting intestinal issues for a while but his condition relapsed recently, forcing The Eagles to pull out of their Kennedy Center Honors appearance in December, 2015.
At the time, the band said he needed major surgery that would require a lengthy recovery.
Don Henley said: “He was like a brother to me; we were family, and like most families, there was some dysfunction. But the bond we forged 45 years ago was never broken.
“We built something that has lasted longer than anyone could have dreamed. But Glenn was the one who started it all.”