Buildings, newspaper front pages and websites across the US and beyond have changed colour in his honour, BBC reported.
Prince was found dead at his Minnesota home on Thursday. He became a superstar in the 1980s, with the albums 1999, Purple Rain and Sign O’ the Times.
No cause of death has been stated and a post-mortem examination will take place on Friday.
US President Barack Obama said the world has “lost a creative icon”.
Prince’s innovative music spanned rock, funk and jazz. He sold more than 100 million records during his career.
In Prince’s native Minneapolis, the Minnesota Twins baseball team turned their stadium purple, as did the Lowry Avenue Bridge in the centre of the city.
Other prominent buildings in New York and New Orleans were also given a new purple look. And while the Niagara Falls were turned purple to mark the Queen’s 90th birthday, the coincidence was welcomed by Prince fans online.
MTV’s Twitter logo has also turned purple. In Britain, the front page of the Sun newspaper featured a photo of Prince against a purple background with the headline: “Purple reign is over”.
Hundreds of people gathered in the centre of Minneapolis into the early hours of Friday. At one point, they all came together to sing Prince’s 1984 hit Purple Rain.
Vigils for the singer were also held outside his home as well as in Los Angeles and Brooklyn, where the film director Spike Lee, a friend of Prince’s, led an impromptu street party.
In a statement, Carver County Sheriff Jim Olson said his deputies responded to a medical call around 9.43 p.m. (local time) and later found an unresponsive adult male in an elevator at Paisley Park Studios.
First responders tried to revive him but he was pronounced dead at 10.07 p.m.
Paisley Park feels like the new Graceland. Prince’s home and recording studio is awash with tears and tributes.
Well into the night, thousands of fans came here to lay flowers, cards and balloons at a makeshift shrine.
Others gathered in central Minneapolis, dancing and singing as they paid their respects to a local and global superstar, whose unique, sexually-charged blend of funk, rock and soul revolutionised music.
Here in the twin cities, Minneapolis and St Paul, there is shock and grief but also pride. One local radio station is urging its listeners to wear purple on Friday in tribute.
Many residents point out that Prince could have lived anywhere in the world. They feel honoured, they say, that he chose to remain until the very end in the place where he was born.
Born in 1958, Prince was a prolific writer and performer from a young age — reportedly writing his first song when he was seven.
He was an arranger and multi-instrumentalist, and recorded more than 30 albums. His best-known hits include Let’s Go Crazy and When Doves Cry.
He also wrote music for other artists. Nothing Compares 2U, written for The Family, was later made famous by Sinead O’Connor in 1990.
In 1984, he won an Oscar for the score to Purple Rain, a film in which he also starred.
Throughout his career he had a reputation for secrecy and eccentricity, once changing his name to an unpronounceable symbol.
In 2004, Prince was inducted into the Rock and Roll Hall of Fame, which said he “rewrote the rulebook”.
He had a mercurial relationship with technology. In 2000, he released singles via the pioneering music-sharing service Napster, but he later declared the internet “completely over” and refused to allow his music on major streaming platforms.
Prince’s latest album, HITnRUN Phase Two, was released last year and he had been touring as recently as last week.
On April 15 he was taken to hospital after his private plane made an emergency landing in Illinois. It happened just hours after he had performed on stage in Georgia. He was treated and released after a few hours.
Tributes have been pouring in from artists young and old, across the musical spectrum.
Madonna, who dated Prince briefly, described him as a “visionary who changed the world”, while Chic guitarist Nile Rogers said there were “tears and love on our tour bus”.
Mick Jagger said Prince’s talent was “limitless”, and called him a “revolutionary artist, a great musician, a wonderful lyricist”.
President Obama said: “Few artists have influenced the sound and trajectory of popular music more distinctly, or touched quite so many people with their talent”.