Steve Strange's record label manager Marc Green confirmed the sad news in a statement.
He said: "We are extremely saddened to announce that Steve Strange died at 11.15 local time on Thursday February 12 in Sharm el-Sheikh International Hospital, Egypt.
"Steve died in his sleep of heart failure.
"Steve's family, band members and friends are all distraught at this sudden news of his untimely death.
"Steve's family request privacy at this extremely difficult time."
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."
Simon Le Bon, the frontman of Duran Duran, also paid tribute on Twitter, writing: "I'm very sad to announce that our friend Steve Strange has died in Egypt today.
"He was the leading edge of New Romantic. God Bless him."
Boy George added: "Heartbroken about the death of my friend Steve Strange. So bloody sad. Such a big part of my life!"
Ex-EastEnders star Martin Kemp, who sings with Spandau Ballet, said: "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.
Our thoughts are with his friends and family at this sad time.