Bronski formed the group in London in 1983 with singer Jimmy Somerville, a fellow Glaswegian, and Larry Steinbachek, who passed away five years ago.
Born Steven Forrest and brought up in the Castlemilk estate, Bronski worked as a labourer and stage hand while playing bass in a Country and Western group before moving south.
He shared a flat with his bandmates in Brixton, south London.
The group began when Bronski and Steinbachek met Somerville through a documentary called Framed Youth - Revenge of the Teenage Perverts, which was made for an LGBTQ arts festival.
The group signed a recording contract after playing just nine gigs but would go to to enjoy several top 10 hits in the UK, including Smalltown Boy, Why? and a cover of Donna Summer's I Feel Love.
Smalltown Boy, their debut single, was particularly groundbreaking for many fans who related to its story of a young, gay man leaving his home town for the freedom of the big city.
The video showed Somerville being chased by a homophobic gang, taken home by the police and thrown out by his parents, before getting on a train to start a new life.
Why was a Top 10 hit for the band in Australia, Switzerland, Germany, France and the Netherlands.
Bronski Beat were one of the few bands of the era to campaign on gay rights issues and their debut album, The Age Of Consent, listed the ages of consent for gay sex in countries around the world. At the time, the age of consent for sex between men in the UK was 21.
Somerville singer left the band in 1995 to form The Communards with Richard Coles but Bronski Beat continued, reaching the top 10 again with Hit That Perfect Beat in November 1985.
The group carried on in the 1980s and 1990s, and in 2017 released their first new album for 22 years, with Bronski as the only remaining original member.
Posting on social media. Somerville said: “Sad to hear Steve Bronski has died.
“He was a talented and a very melodic man. Working with him on songs and the one song that changed our lives and touched so many other lives, was a fun and exciting time. Thanks for the melody Steve."
In an interview three years ago, Bronski said: "At the time we were just three gay guys who started a band - we didn't feel like part of any particular movement.
"Of course, it would transpire many years later that there were more gay artists than the public were led to believe."
In a separate interview two years ago, he said: "Very few pop acts were speaking out about the struggles of the gay community in their day-to-day lives.
"For us, it was a lot easier living in London, since there was a thriving gay scene compared to other parts of the country. The press didn’t help in their approach to AIDS.
“We were just three openly gay men writing songs about our lives. A lot of people in our community just happened to relate to our songs, which was amazing.”