He made 33 appearances for Tigers between 1945 and 1948.
Peter Wheeler, Leicester Tigers executive director, said: "We were saddened to hear of Peter Tahany's passing. He served Leicester Tigers well as a player in the years immediately after the Second World War and played in just about every position in the forward pack, which says a lot about his commitment to the club."
Away from rugby, Peter Tahany founded Wigston aerospace parts manufacturer Northbridge and became chairman of its parent company, Linread. A Freeman of the City of London, he also played an active role in a number of business and community groups.
Leicester Tigers pass on condolences to Peter's family and friends. His funeral is at 12.30pm on Friday (October 1) at Holy Cross Priory Church, Wellington Street, Leicester.