The Liverpool-born shot-stopper joined Town from Manchester City in March 1971. He passed away peacefully in his sleep today.
He made 370 league appearances for the club and 432 appearances in all competitions.
Mulhearn continued to live locally and until very recently he worked alongside Town's commercial and hospitality teams on matchday.
He won two promotions with Shrewsbury, from Division Four as runners-up in 1975 and as champions of Division Three in 1979
The custodian was one of 10 legends initially inducted into the Shrewsbury Hall of Fame in 2011.
Chairman Roland Wycherley said: "Our thoughts and condolences go out to his family and friends at this sad time.
“Ken was a true Shrewsbury Town legend on the pitch and was a very popular person around the club and town.
“He will be remembered fondly for his performances in a Town shirt and for being part of the side that helped the club to what is now the Championship.
“He continued to work around the club on matchday and will be greatly missed.”
Funeral details will be released in due course and the family have asked that any donations should be passed on to Parkinson’s UK.