Musician and his New York group influenced generations of bands with mixture of European and US styles of sound and art
He had been suffering from liver failure and received a transplant earlier this year.
Reed's literary agent, Andrew Wylie, said the musician died on Sunday morning in Southampton, New York, of an illness related to the transplant. His UK music agent, Andy Woolliscroft, confirmed the news to the Guardian earlier on Sunday night, saying: "Yes I'm afraid it's true. I'm very upset."
John Cale, his longtime friend and a founding member of the Velvet Underground, said: "The world has lost a fine songwriter and poet … I've lost my school-yard buddy."
Tributes from musicians and writers were quick to appear on social media.
David Bowie said on his Facebook page: "He was a master." Iggy Pop called it "devastating news". Kim Gordon of Sonic Youth wrote: "So sorry to hear of Lou Reed's passing this is a huge shock!" The chef and author Anthony Bourdain quoted the Velvet Underground's song Sweet Jane: "'Heavenly wine and roses … seem to whisper to me … when you smile' … RIP Lou Reed." Lloyd Cole wrote: "Without Lou there is no Bowie as we know him. Me? I'd probably be a maths teacher." Ryan Adams said only: "Lou Reed."
Nile Rodgers of the funk band Chic tweeted: "Lou Reed, RIP I did the Jools Holland show with him last year and we yucked it up. I didn't know he was ill."
The writer Salman Rushdie opted to commemorate the singer in a message heavy with references to his songs: "My friend Lou Reed came to the end of his song. So very sad. But hey, Lou, you'll always take a walk on the wild side. Always a perfect day."
Fans also piled on to Reed's Facebook page to leave tributes. "One of the greatest men I ever met and one of the kindest and most loving – and that's from someone who worked with him and knew him since the 1960s," wrote one.
Another said: "A sad day, not a perfect day at all. RIP., Lou. You'll never know what your words and music did for me and what an influence you had on the way I think."
Although the Velvet Underground never achieved great commercial success, their idiosyncratic mixture of harsh guitars and smooth melodies sung by Reed or model Nico proved enduring.
The band's influence on rock, art rock and punk was memorably summed up by Brian Eno's observation that although the first Velvet Underground album may have sold only 30,000 copies in its first few years, "everyone who bought one of those 30,000 copies started a band".
After making his name with the Velvet Underground and forming part of Andy Warhol's Factory scene in New York, Reed entered the similarly decadent orbit of David Bowie and Iggy Pop in the early 1970s and recorded a series of seminal and sometimes challenging solo albums including Transformer, Berlin and Metal Machine Music.
A heavy drinker and drug user for many years, Reed had a liver transplant this year at the Cleveland Clinic.Lou Reed's experimental nature influenced several musical genres from punk to electronica.
In June, his wife, Laurie Anderson, revealed just how ill he had been. "It's as serious as it gets," she told the Times. "He was dying. You don't get it for fun."
Despite his illness, however, Reed had appeared to make a rapid recovery. "I am a triumph of modern medicine, physics and chemistry," Reed wrote on his website a few weeks after his surgery. "I am bigger and stronger than ever. My chen tai chi and health regimen has served me well all of these years … I look forward to being on stage performing, and writing more songs to connect with your hearts and spirits and the universe well into the future."
But he also admitted that old age was taking its toll on his body. Appearing at the Cannes Lions international festival of creativity four months ago, Reed remarked on his increasing frailty. "How could time go that quickly? It never ceases to amaze me," he said. "The other day I was 19, I could fall down and get back up. Now if I fall down you are talking about nine months of physical therapy."
However, he also found time to rail against the quality of digital music – which he said sounded "like shit" – and at the amount of money artists received for music downloads.
Neither age nor illness ever succeeded in blunting Reed's confrontational edge. Reacting to details of the NSA surveillance programme revealed by the whistleblower Edward Snowden, he said it was "beyond belief" that the then 29-year-old could access the data and was able to release it.
"Wow. Does that speak well for our security or what?" he said. "It's so shocking. Obama of all people having that thing going on … A lot of the things [George W] Bush would have done, Obama has continued. How did that happen?"
Reed, whose lack of patience with the press was legendary, could not resist laying into the "parasitical side" of journalists. What they really want is something controversial."Asked by one reporter how he managed to stayed creative, he shot back: "How do I stay creative? I masturbate every day. OK?"