Liverpudlian Davies, who turned 81 last month, guided Town to Third Division championship in his first season in charge in the 1993/94 season.
He also led Shrewsbury to Wembley for the first time in their history in April 1996, where Town lost 2-1 to Rotherham United in the final of the Auto Windscreens Shield.
Davies spent more than a decade as goalkeeper – making more than 100 appearances for both Wolves and Bournemouth – before beginning his coaching career with Norwich City and Swansea and moving into management.
Lovely memories of 93/94 and the 16 game unbeaten run. Team full of confidence, togetherness and believe. Just started to go more often and great season to enjoy. Thank you Fred. Rest in peace.— Lewis Jones (@ShrewsLewis) September 3, 2020
RIP Fred Davies what a season 93/94 season was 💙🧡💙🧡— alban heiron (@albanheiron) September 3, 2020
He took over at Gay Meadow first as caretaker after John Bond's resignation in May 1993 before taking the job full-time in January 1994.
The 93/94 season remains Shrewsbury's last title success and was a memorable campaign for a generation of Salopians as Davies's side saw off rivals Chester and Crewe to finish top of the fourth tier by five points.
Town overcame a stuttering start to that glorious season, going four league games without a win including three defeats. But Davies's side turned it around in style, entertaining fans with the width supplied by two natural wingers.
Davies twice steered Town clear of relegation in the Second Division before Town dropped back to the Third Division at the end of the 1996/97 season, at the end of which he was relieved of his duties.
He had two seasons in charge of non-league Weymouth between 1997 and 1999, in which he led them to the Southern Premier League title.
The League Managers Association (LMA) confirmed Davies' passing, and chairman Howard Wilkinson said: "As a goalkeeper, a coach and a manager, Fred’s successes were all earned the hard way, as was the respect of his peers. He was a credit to the professional game.”
LMA chief executive Richard Bevan added: “Fred’s contribution, impact and influence on English football was vast, most notably in his role as manager of Shrewsbury Town."