The producer's son James - guitarist in Does It Offend You Yeah? - confirmed on Facebook that his father passed away on Saturday.
"It is with great sadness that someone very close to us has passed away," a post on the band's official page read.
"Martin Rushent was not just James' dad, but also someone very involved with the shaping of DIOYY and countless other musicians he worked with. He had an amazing character and was [a] great friend to all of us. Rest in peace, sitting at your mixing desk in the sky. X"
Rushent is survived by his wife Ceri, sons James and Tim and daughters Amy and Joanne.
The producer was known for his work with The Stranglers, The Human League, Buzzcocks, The Go-Gos and XTC, among others. He more recently produced the second Pipettes album Earth vs. The Pipettes.
Mark Ronson said on Twitter: "Just read the sad news about Martin Rushent. The production on DARE by Human League is one of the crowning moments of SynthBritannia. RIP."
On his website, ex-Stranglers star Hugh Cornwell said: "It is with great sadness that I hear of Martin Rushent's passing.
"He was a vibrant and gifted individual who was able to extract the essence of what The Stranglers began with, and translate it into something that could be played on radios across the UK.
"It was obviously no one-off success, as he was later to show with The Human League. I remember him fondly."
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