The right-back made 205 appearances for the club, scoring twice during five years at The Hawthorns.
The England international also collected a 1954 FA Cup-winners' medal after playing in every round before missing out on the final due to injury.
Albion will pay tribute to the defender at Saturday's home game against Manchester United.
The club said in a statement: "Our thoughts are with Stan's family and friends at this difficult time.
"The club will pay tribute to Stan's career at Saturday's home game with Manchester United."
Stan emigrated to Australia in 1969 where he stayed.
His death, shortly before his 90th birthday, cuts the final connection with Albion's grandly-named 'team of the century' of 1953-54, the side coming within a whisker of carrying off the 20th century's first League and FA Cup double, an ambition only halted by an injury crisis in the final weeks of the campaign and they finished runners-up to Wolves.
Along with goalkeeper Norman Heath, Stan missed out on the FA Cup final at Wembley when Albion beat Preston 3-2.
Born in Stockton-on-Tees, Rickaby joined Albion from Middlesbrough for £7,500 in February 1950, initially as reserve to Jim Pemberton.
But he soon replaced him, playing 143 consecutive league games from August 1950 to November 1953.
His first goal came on Christmas Day 1952, in a 3-2 defeat at Bolton, the second in a 4-2 triumph over Sheffield Wednesday in February 1954.
After missing out on the Cup final, he returned to the side at the start of the following season, though he was now embroiled in a real fight for the shirt with Stuart Williams, while the youthful Don Howe was also appearing on the horizon.
Leaving Albion at the end of the 1954-55 campaign, aged 31, he was player-manager at Poole Town for a time, and later played for Weymouth and Newton Abbott Spurs before retiring in 1964 and going into business.