Joe bravely battled a debilitating illness and throughout maintained a close interest in the company," said chairman Peter Maunder.
B&T was a "major part of his life", added Maunder, whose former colleague was with the firm 55 years and was a descendent of Joseph Tanner, who co-founded the company in the 1860s.
"Joe was a magnificent, literary man and fond of the arts. He loved books and was wonderful to know and work for. He was much loved and will be missed dearly."
Joe Tanner leaves wife Gerry and children Amanda, Jeremy and Tom. The funeral is in Bruton on 18 April.
B&Ts Tanner passes away
Print legend Joe Tanner, the former non-executive director of Butler and Tanner, died last week aged 78.