Frey “fought a courageous battle” for the past several weeks, according to his publicist, but succumbed to complications from rheumatoid arthritis, acute ulcerative colitis and pneumonia.
“Words can neither describe our sorrow, nor our love and respect for all that he has given to us, his family, the music community & millions of fans worldwide,” his publicist said.
Guitarist Frey and drummer Don Henley formed the Eagles in Los Angeles the early 1970s, along with guitarist Bernie Leadon and bassist Randy Meisner. They would become a top act over the next decade, embodying the melodic California sound.
Henley said in a statement Frey was "like a brother to him."
"The bond we forged 45 years ago was never broken, even during the 14 years that the Eagles were dissolved, he said. "We were two young men who made the pilgrimage to Los Angeles with the same dream: to make our mark in the music industry - and with perseverance, a deep love of music, our alliance with other great musicians and our manager, Irving Azoff, we built something that has lasted longer than anyone could have dreamed."
An Eagles greatest hits collection from the mid-1970s and "Hotel California" are among the best-selling albums in history.
Frey was born in Detroit and was raised in its suburbs. His solo hits include "The Heat Is On" and "Smuggler's Blues."
Frey was lead vocalist on the Eagles' breakthrough hit, "Take It Easy," a song mostly written by Jackson Browne that came out in 1972. His other showcases included "Peaceful Easy Feeling," "Already Gone" and "New Kid in Town."
The Eagles split up in 1980 but reunited in 1994 and were one of the world's most popular concert acts. The band, which for years was made up of Frey, Henley, Joe Walsh and Timothy B. Schmit, was supposed to have been honored at the Kennedy Center last month. But the appearance was postponed because of Frey's health problems.
Frey, known for his oversized jaw, big grin and blunt personality, loved music, girls and the rock 'n' roll life. He would meet up with Henley, Meisner and Leadon while all were trying to catch on in the Los Angeles music scene, and for a time the four backed Linda Ronstadt. They also befriended such other Los Angeles-based musicians as Browne and J.D. Souther, who would collaborate on "New Kid in Town" and other Eagles songs.
They harmonized memorably on stage and on record but fought often otherwise. Leadon and Meisner departed after run-ins with Frey, and guitarist Don Felder, who had joined the group in 1974, ended up in legal action with the Eagles.
Frey and Henley also became estranged for years, their breach a key reason the band stayed apart in the 1980s. Henley had vowed the Eagles would reunite only when "hell freezes over," which became the name of the 1994 album they never imagined making.
The Associated Press contributed to this report