The Welsh New Romantic icon - best known for the hit Fade To Grey - died in hospital in Sharm el-Sheikh, Egypt.
Ex-Visage bandmates Midge Ure and Rusty Egan said they were "devastated" to hear of his "untimely passing", adding: "Steve was a major face of the 80s."
Boy George tweeted he was "heartbroken" about the death of Strange, saying he was "such a big part of my life".
Duran Duran frontman Simon Le Bon tweeted that Strange was "the leading edge of New Romantic. God Bless him".
Fellow 1980s pop star Billy Idol tweeted: "Very sad to hear of my friend Steve Strange passing, RIP mate."
Spandau Ballet guitarist Gary Kemp dedicated the band's performance in Italy to "a maverick to the end", while his brother and the band's bassist, Martin Kemp, tweeted: "RIP Steve Strange goodbye my dear friend. I will miss you!"
Strange's agent, Pete Bassett, said he would be remembered as "a hard-working, very amusing and lovable individual who always was at the forefront of fashion trends".
"Up until last year he was putting together a book of fashion styles based on the New Romantic movement and it comes as a great shock.
"We understood that he had certain health problems but nothing we knew was life threatening.
"His friends and family are totally shocked, we had no idea anything like this was likely to happen."
He had suffered ill-health, including in December last year when he was admitted to Princess of Wales Hospital, in Bridgend, with a bronchial infection and an intestinal blockage.
By pop singer Kim Wilde
Steve took me out on a date to the iconic Langan's Brasserie in Mayfair right at the beginning of my career in 1981.
I was very in awe of him only having just met him, but we quickly became friends and laughed at ourselves ordering sausage and mash with champagne.
As we left, the press descended on us, we both pouted furiously and headed off to The Blitz club where we bumped into Marilyn and a host of exotic, beautiful New Romantics, drank vodka and crashed out at his apartment in Notting Hill.
When I woke up in the spare room the next morning, I wandered through his elegant apartment to find him asleep with his eye mask on. I guess he didn't get to be that flawless without a beauty regime, he certainly had looked far more glamorous than I did the previous evening.
Steve will be remembered as the most elegant and beautiful of the New Romantics at the beginning of the 80s. I'm so grateful that life brought Steve and I together, he was funny, great company and completely bonkers in the most adorable way.
Born Steven Harrington, in Newbridge, Caerphilly county, Strange got involved in music after seeing the Sex Pistols in concert in 1976.
He went to London aged 15 to work for Sex Pistols manager Malcolm McClaren before co-founding the Blitz Club in Soho, central London, which would become a focal point for the New Romantic movement.
Bands including Duran Duran, Spandau Ballet and Culture Club all got their start at the club before finding stardom.
His band, Visage, formed in 1979 and their breakthrough single, Fade To Grey, peaked at number eight in the UK in 1981.
It reached number one in both Germany and Switzerland, and was the first of five UK top 40 hits for the band, which also numbered Midge Ure and Rusty Egan among its members.
Strange also starred in the video of his good friend David Bowie's number one single Ashes to Ashes in 1980. At the time, the futuristic mini-film was hailed as the most expensive pop music video in history.
Strange - who admitted he faced drug addiction problems in the years that followed his early success - recorded a new Visage album, called Hearts and Knives, in May 2013, with the band boasting a new line-up. The band also recorded a new classical interpretation of Fade To Grey last year.
In the intervening years, he had become a sought-after commentator on pop culture, appearing on a number of TV shows recalling the New Romantic era.
In a nod to his involvement in the Ashes to Ashes single, he appeared as himself in the BBC One police drama of the same name.
He also made a series of memorable appearances in BBC3 reality show Celebrity Scissorhands, winning the first series in 2007 and returning the following year as an "image consultant".
Steve Strange, lead singer of 1980s pop band Visage, has died aged 55 following a heart attack, his record label says.