Foulkes joined United in 1950 and went on to make 688 appearances for the club during 18 seasons, winning four league titles as part of manager Matt Busby's side.
He was also part of the 1968 European Cup winning team.
"Bill was a giant character in the post-war history of Manchester United. His contribution over almost 700 games and nearly 20 years will never be forgotten," Ed Woodward, United's executive vice-chairman said on the club's website (www.manutd.com).
"He was a very gentle man, whom I was privileged to meet on several occasions, including most memorably with his team mates at the Champions League final in Moscow, 50 years after his heroics in the Munich air crash."
Eight players and three club officials were among 23 people who died when the plane carrying them home from a European Cup tie in Belgrade crashed after refuelling at Munich Airport on Feb. 6 1958.
Bobby Charlton, who survived and went on to help England win the 1966 World Cup, later recalled coming round from being knocked unconscious and realising that Foulkes and fellow player Harry Gregg were helping people to escape from the plane wreckage.
"It was a very brave thing to do, the plane was on fire and broken in half," he was quoted as saying on manutd.com. "Those two ought to be thanked for what they did."