His body was discovered at his Paisley Park home in Minnesota early yesterday, his publicist confirmed.
Prince, whose real name was Prince Rogers Nelson, suffered a medical emergency earlier this month.
The ‘Purple Rain’ singer was flying home from a show in Atlanta, Georgia, on April 15 when he was taken ill and his private jet made an emergency landing in Molina, Illinois.
He was taken to a nearby hospital by ambulance, where he was treated and released hours later.
At the time, a representative for Prince assured fans he was feeling much better and was resting at home.
Carver County Sheriff’s Office confirmed it was investigating the death.
Audio of the emergency services dispatch call asked for paramedics to go to 7801 Audobon Road and describes a “male down, not breathing”.
Fans soon gathered across the road from his home in the rain, with a number of dark-coloured cars parked inside the Paisley Park compound.
Tributes flooded in Prince. Chic frontman Nile Rodgers tweeted: “RIP our dearly beloved Prince. Tears and love on our tour bus... I’ll never forget my brother. We’ve had good times.”
Madonna, who collaborated with Prince on ‘Love Song’ on her album Like A Prayer, posted a picture of the two of them together on Instagram, writing: “He Changed The World!! A True Visionary. What a loss. I’m Devastated.”
Chaka Khan posted a picture of herself with Prince on Twitter: “I LOVED him, the world LOVED him. Now he’s at peace with his Father. Rest in power, @prince, my brother.”
Rolling Stone Ronnie Wood wrote: “I will miss a good friend who was so talented. He was such a great performer/guitar player. Sleep well Prince.”
Music producer Quincy Jones tweeted: “RIP to @prince... a true artist in every sense of the word. Gone way too soon.”
Film director Spike Lee wrote on Instagram: “I Miss My Brother. Prince Was A Funny Cat. Great Sense Of Humor.”
Model Iman, who lost her husband David Bowie earlier this year, wrote: “So sad to hear of Prince’s passing; one of the greatest musical talents of my lifetime. Maybe of the 20th century. RIP.”
Justin Timberlake wrote a heartfelt post on Instagram: “They say don’t meet your idols... That they let you down. But, some of my greatest, funniest (yes, he was hilarious), and most prolific encounters and conversations about music came from the moments that I spent with him. It would be silly to say that he has inspired our music... It’s beyond that. He’s somewhere within every song I’ve ever written.”
The Rev Jesse Jackson praised Prince for fighting for the freedom of artists and for himself, calling him “a transformer”.
Prince was widely regarded as one of the most inventive musicians of his era and many of his songs are seen as classics.
He became an international superstar in 1982 after his breakthrough album 1999 and was most famous for hits including ‘Purple Rain’, ‘When Doves Cry’, and ‘Kiss’.
His career spanned more than three decades and he won seven Grammy Awards, sold more than 100m records, and won an Oscar for Best Original Song Score for ‘Purple Rain’.
Prince, who was just 5ft 2in, was an eccentric with a tendency towards bizarre career moves, such as changing his name to an unpronounceable symbol in the 1990s.
He was in the process of writing an untitled autobiography which was due to be published in 2017.
He became even more famous with the release of the film Purple Rain in 1984, a seemingly autobiographical movie set in the club scene in his home town of Minneapolis.
It was a huge success and the soundtrack album spent 24 weeks at the top of the charts and sold more than 13m copies.
It was the first time in his career that Prince had recorded with, and credited, his backing band, which he named the Revolution.
He was fiercely protective of his independence, battling his record company over control of his material and even his name.
Prince once wrote “slave” on his face in protest at not owning his work and battled with and then departed from his label, Warner Bros, before returning a few years ago.
He was married twice, the first time to his backing dancer Mayte Garcia, from whom he split in 2000, and then Manuela Testolini, whom he divorced in 2006.
Prince was inducted into the Rock and Roll Hall of Fame in 2004, where he was hailed as a trailblazer.
The dedication reads: “He rewrote the rulebook, forging a synthesis of black funk and white rock that served as a blueprint for cutting-edge music in the eighties.
“Prince made dance music that rocked and rock music that had a bristling, funky backbone. From the beginning, Prince and his music were androgynous, sly, sexy and provocative.”
He played a 21-night stint at the O2 Arena in London in the summer of 2007. On his last night, Prince declared: “Everything’s changed this summer. It doesn’t matter who came before or who comes after. From now on, the O2 is Prince’s house.”
Stars from Madonna to Justin Timberlake pay tribute to the singer and guitarist