Reed died in Southampton, New York, of an ailment related to his recent liver transplant, according to his literary agent, Andrew Wylie, who added that the star had been in frail health for months.
Reed shared a home in Southampton with his wife and fellow musician Laurie Anderson, whom he married in 2008.
Reed never approached the commercial success of such superstars as the Beatles and Bob Dylan, but no songwriter to emerge after Dylan so radically expanded the territory of rock lyrics.
No band did more than the Velvet Underground to open rock music to the avant-garde - to experimental theatre, art, literature and film, to William Burroughs and Kurt Weill, to John Cage and Andy Warhol, Reed's early patron.
Indie rock essentially began in the 1960s with Reed and the Velvets; the punk, New Wave and alternative rock movements of the 1970s, '80s and '90s were all indebted to Reed, whose songs were covered by R.E.M., Nirvana, Patti Smith and countless others.
"The first Velvet Underground record sold 30,000 copies in the first five years," Brian Eno, who produced albums by Roxy Music and Talking Heads among others, once said. "I think everyone who bought one of those 30,000 copies started a band!"
Reed's trademarks were a monotone of surprising emotional range and power; slashing, grinding guitar; and lyrics that were complex, yet conversational, designed to make you feel as if Reed were seated next to you.
Known for his cold stare and gaunt features, he was a cynic and a seeker who seemed to embody downtown Manhattan culture of the 1960s and 70s and was as essential a New York artist as Martin Scorsese or Woody Allen.
Reed's New York was a jaded city of drag queens, drug addicts and violence, but it was also as wondrous as any Allen comedy, with so many of Reed's songs explorations of right and wrong and quests for transcendence.
He had one top 20 hit, Walk On the Wild Side, and many other songs that became standards among his admirers, from Heroin and Sweet Jane to Pale Blue Eyes and All Tomorrow's Parties.
An outlaw in his early years, Reed would eventually perform at the White House, have his writing published in The New Yorker, be featured by the Public Broadcasting Service in an American Masters documentary and win a Grammy in 1999 for Best Long Form Music Video.
The Velvet Underground was inducted into the Rock and Roll of Fame in 1996 and their landmark debut album, The Velvet Underground & Nico, was added to the Library of Congress' registry in 2006.
Reed called one song Growing Up in Public and his career was an ongoing exhibit of how any subject could be set to rock music - the death of a parent (Standing On Ceremony), Aids (The Halloween Parade), some favourite movies and plays (Doin' the Things That We Want To), racism (I Want to be Black) and the electroshock therapy he received as a teen (Kill Your Sons).
He was one of rock's archetypal tough guys, but he grew up middle class - an accountant's son raised on Long Island, east of New York City.
Reed was born to be a suburban dropout. He hated school, loved rock 'n' roll, fought with his parents and attacked them in song for forcing him to undergo electroshock therapy as a supposed "cure" for being bisexual. "Families that live out in the suburbs often make each other cry," he later wrote.
His real break began in college. At Syracuse University, he studied under Delmore Schwartz, whom Reed would call the first "great man" he ever encountered.
He credited Schwartz with making him want to become a writer and to express himself in the most concrete language possible.
Reed honoured his mentor in the song My House, recounting how he connected with the spirit of the late, mad poet through a Ouija board. "Blazing stood the proud and regal name Delmore," he sang.
Reed moved to New York City after college and travelled in the pop and art worlds, working as a house songwriter at the low-budget Pickwick Records and putting in late hours in downtown clubs. One of his Pickwick songs, the dance parody The Ostrich,was considered commercial enough to record.
Fellow studio musicians included a Welsh-born viola player, John Cale, with whom Reed soon performed in such makeshift groups as the Warlocks and the Primitives.
They were joined by a friend of Reed's from Syracuse, guitarist-bassist Sterling Morrison; and by an acquaintance of Morrison's, drummer Maureen Tucker, who tapped out simple, hypnotic rhythms while playing standing up.
They renamed themselves the Velvet Underground after a Michael Leigh book about the sexual subculture.
By the mid-1960s, they were rehearsing at Warhol's "Factory," a meeting ground of art, music, orgies, drug parties and screen tests for films that ended up being projected onto the band while it performed, part of what Warhol called the Floating Plastic Inevitable.
The Velvets said everything other bands were forbidden to say and some things other bands never imagined.
Reed wrote some of rock's most explicit lyrics about drugs (Heroin, 'Waiting for My Man), sadomasochism (Venus in Furs) and prostitution (There She Goes Again).
His love songs were less stories of boy-meets-girl, than ambiguous studies of the heart, like the philosophical games of Some Kinda Love or the weary ballad Pale Blue Eyes, an elegy for an old girlfriend and a confession to a post-breakup fling.
The mainstream press, still seeking a handle on the Beatles and the Rolling Stones, was thrown entirely by the Velvet Underground. The New York Times at first could not find the words, calling the Velvets "Warhol's jazz band" in a January 1966 story and "a combination of rock 'n' roll and Egyptian belly-dance music" just days later.
At Warhol's suggestion, they performed and recorded with the sultry, German-born Nico, a "chanteuse" who sang lead on a handful of songs from their debut album.
A storm cloud over 1967's Summer of Love, The Velvet Underground & Nico featured a now-iconic Warhol drawing of a (peelable) banana on the cover and proved an uncanny musical extension of Warhol's blank-faced aura.
Reed made just three more albums with the Velvet Underground before leaving in 1970. Cale was pushed out by Reed in 1968 (they had a long history of animosity) and was replaced by Doug Yule.
Their sound turned more accessible, and the final album with Reed, Loaded, included two upbeat musical anthems, Rock and Roll and Sweet Jane.
He lived many lives in the '70s, initially moving back home and working at his father's office, then competing with Keith Richards as the rock star most likely to die.
He binged on drugs and alcohol, gained weight, lost even more and was described by critic Lester Bangs as "so transcendently emaciated he had indeed become insectival."
His albums in the '70s were alternately praised as daring experiments or mocked as embarrassing failures, whether the ambitious song suite Berlin or the wholly experimental Metal Machine Music, an hour of electronic feedback.
But in the 1980s, he kicked drugs and released a series of acclaimed albums, including The Blue Mask, 'Legendary Hearts and New Sensations.
He played some reunion shows with the Velvet Underground and in 1990 teamed with Cale for Drella, a spare tribute to Warhol.
He continued to receive strong reviews in the 1990s and after for such albums as Set the Twilight Reeling and Ecstasy, and he continued to test new ground, whether a 2002 concept album about Edgar Allan Poe, The Raven, or a 2011 collaboration with Metallica, Lulu.