Les Winwood was a councillor for Bridgnorth West and Tasley and served the area for over 40 years.
Mr Dunne said he was shocked and saddened by the news, calling him a 'dedicated public servant' and 'loyal friend to Bridgnorth'.
Councillor Winwood had served on Bridgnorth District Council and Bridgnorth Town Council and was elected to the unitary authority representing Bridgnorth and Tasley in 2009. In total he had served the area for 43 years,
Shropshire Councils's leader Lezley Picton announced the news at a cabinet meeting and said it was a 'very sad day' for the authority and those who knew Councillor Winwood.
She said: "Having known him as both an officer and a member, he never changed. He was as delightful to you as when I was an officer as he was when I was a member, and he has showed me tremendous support since I became leader.
"Les absolutely loved where he lived and he loved the people who live there, and he worked tirelessly for them.
"It is a very sad day."
Councillor Kirstie Hurst-Knight, who serves Bridgnorth East and Astley Abbots had known Mr Winwood since she was a child, due to him being a colleague of her father John.
She said: "It is just such a shock to hear the news, I knew Les as both a friend and colleague of my father and as a fellow councillor.
"The service he gave to Bridgnorth - an area which he loved and always lived in - will probably never be surpassed. He dedicated a large part of his life to it and will be a big miss for people in the town."
Former Bridgnorth mayor Ron Whittle described Mr Winwood as a 'stalwart' of the town and said his personality and work would be much missed.
He said: "Whatever your political affiliation it would be recognised that Les worked tirelessly for the area whichever council he was on and showed dedicated service of over 40 years."