Capel, who was 87, was a key member of the Reds side that won the Third Division South title in 1951. He scored 24 goals during that promotion-winning season, including four in a 9-2 win over Gillingham at the City Ground.
An inside left, he scored 72 goals in 162 appearances during just over four years at the club.
Forest chief executive Mark Arthur said: "The club would like to extend its sincere condolences to Tommy's family and friends at this sad time.
"Tommy's contribution to the club's promotion success in the early 1950's won't ever be forgotten."
Capel also played for Manchester City, Chesterfield, Birmingham, Coventry and Halifax.