The full-back was part of the Wales squad at the 1958 World Cup in Sweden, playing in all of the group matches before the team were knocked out by Brazil in the quarter-finals.
Williams won 43 international caps and also skippered his country 14 times, making his final appearance in 1965.
He started his career with hometown club Wrexham before joining West Brom in 1950.
Williams enjoyed a distinguished 12-year career with the Baggies, playing in 226 games, and he then saw out his career with Southampton.
He scored three goals in 150 appearances for the Saints before retiring in 1966 after helping the club gain promotion to the top flight for the first time in their history.
He moved into coaching after hanging up his boots and held roles with West Brom, Aston Villa, Morton and Southampton, as well as managing sides in Iran and Norway.
A statement on the Football Association of Wales website read: "The FAW is saddened to announce the passing of former international captain, Stuart Williams, aged 83."
A West Brom statement added: "Stuart was a loyal servant to the club, making almost 250 appearances and scoring nine goals during a 12-year spell as a player.
"The Wales defender remained Albion's most capped international until last season and was also 'reserve' for the 1954 FA Cup final success and 'trainer' when the club next lifted the trophy 14 years later.
"Our thoughts are with Stuart's two sons, Neil and Paul, and the rest of his family and friends at this difficult time. The club will pay tribute to Stuart's career at our next home game against Aston Villa on Monday, November 25."