Tapscott made 14 Wales appearances after being signed from Barry by Arsenal for £2,750 in 1953.
He scored 68 goals in 132 Gunners league and cup games and 101 in 234 competitive Bluebirds matches.
Tapscott played for the Bluebirds from 1958 to 1965, then for Newport County, Cindeford, Haverfordwest and Carmarthen Town before retiring at the age of 39.
A Cardiff City spokesman said: "We would like to pass on our sincere condolences to everyone who was fortunate to have known 'Tappy'."
Tapscott leaves his wife, Glenys, two daughters and three grandchildren.
Source: BBC