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The band's catchy songs and tartan-heavy outfits made them famous among teenagers around the world in the 1970s.
McKeown sang the Scottish band's biggest hits including Bye, Bye, Baby, Shang-a-lang and Saturday Night, which reached No 1 on the US Billboard Hot 100.
"'It is with profound sadness that we announce the death of our beloved husband and father Leslie Richard McKeown," said the statement on the band's official Facebook page.
"Leslie died suddenly at home on Tuesday, April 20, 2021. We are currently making arrangements for his funeral."
The Bay City Rollers sold more than 100 million records and cut a distinctive swath through the music industry with their tartan outfits and upbeat brand of pop-rock.
The band's classic line-up featured McKeown, with Alan Longmuir, Eric Faulkner and Stuart Wood on guitar with Derek Longmuir on drums.
They split in 1978 but a reformed version of the group toured New Zealand in 2018.
McKeown also went on to have a successful solo career.
Two other former members of the band, original bassist Alan Longmuir and his replacement Ian Mitchell, have also died in recent years.
- Reuters and NZ Herald