Simpson had endured a "long battle with lung disease", his manager Tessa Le Bars said, reported BBC.Com.
"Having had the privilege of working with Alan and Ray for over 50 years, the last 40 as agent, business manager and friend, and latterly as Alan's companion and carer, I am deeply saddened to lose Alan after a brave battle with lung disease," Le Bars added.
The writer was renowned for creating sitcoms including "Hancock's Half Hour" and "Steptoe and Son", with partner Ray Galton.
Both series were revived in the year 2016 as part of the BBC's Lost Sitcoms series.
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When contacted, Galton and his family said, that right from their beginning "at humour in Milford sanatorium, through a lifetime of work together, the strength of Alan and Ray's personal and professional bond was always at the heart of their success".
The duo went on to write scrips for TV, films and stage for stars such as Peter Sellers, Leonard Rossiter and Frankie Howerd.
They were bestowed with the BAFTA fellowship honour last year and were made OBEs in 2000.
Tributes poured in for Simpson.
Comic Paul Merton said, "Long before I met him, Alan Simpson was a comedy hero of mine. In the flesh he didn't disappoint."
Writer Neil Gaiman tweeted, "I was lucky enough to meet & interview him & Ray Galton in 1985.