Reed, responsible for chart hits including Walk on the Wild Side and Perfect Day, had undergone a life-saving liver transplant earlier this year.
He died of a liver-related ailment, according to his literary agent, Andrew Wylie, who added that the star had been in frail health for months.
Tributes flooded in from the world of showbusiness. John Cale, the Welsh-born musician who co-founded the Velvet Underground but had a sometimes fractious relationship with his former bandmate, released a statement on his Facebook page. "The world has lost a fine songwriter and poet. I've lost my 'school-yard buddy'," he said.
Singer Marianne Faithfull described Reed as a "great friend, musician, songwriter and band leader".
She said he was "one of the most intelligent musicians I've ever known and a great guitarist", adding: "He was a genius. I will miss him terribly."
The Who's official Twitter feed said simply: "RIP Lou Reed. Walk on the peaceful side."
Edinburgh author Irvine Welsh said: "Sad to hear about Lou Reed. RIP Lou and thanks for giving us Perfect Day for Trainspotting."
The Velvet Underground, who were active in the 1960s and 1970s, became known for their fusion of art and music, including early collaborations with the godfather of Pop Art, Andy Warhol.
Despite modest sales during their time together, the band developed a cult following and enjoyed posthumous acclaim. The band are regularly cited as among the greatest influences on contemporary rock music.
Reed, who was notoriously publicity shy, spoke at length of his past alcohol and drug use, anecdotally recalled in the likes of the seven-minute ode to the class A drug Heroin, while Venus in Furs and I'm Waiting for the Man detailed sado-masochistic sex and drug dealing.
As a solo artist, his work was revered. His greatest UK success came when a version of his single Perfect Day was re-recorded for charity in 1997. The record spent three weeks at No 1 in the UK.
More recently, Reed enjoyed chart success with Lulu, a musical collaboration with metal band Metallica.
He underwent a liver transplant earlier this year. In a message posted on his website on June 1, he wrote: "I am a triumph of modern medicine. 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."
The last tweet sent on Reed's official Twitter account, hours before news of his death emerged, simply said "The Door". The tweet links through to a picture of a door, with a poster of Reed on it.
He passed away at a home he shared in Long Island, New York, with his musician wife Laurie Anderson.
Iggy Pop's official Twitter account called the news "devastating", while musician Kim Gordon of Sonic Youth tweeted: "So sorry to hear of Lou Reed's passing this is a huge shock!"