Keki Jessavala (64) protested his innocence and fought to overturn a conviction and three-month prison sentence, suspended for a year, imposed in January.
As Mr Jessavala was appealing he was allowed to retain his seat in the Fleet division. He was one of the longest serving members, having first been elected in 1981.
Police have confirmed there were no suspicious circumstances surrounding the death on 28 July. The North Hampshire coroner is treating it as a death by natural causes so there will be no inquest.