The centre-back, who died in the early hours of Monday morning, became captain of the club following the plane crash in Munich which claimed the lives of 23 people, and played a key role in their 1967/68 European Cup triumph, the first by an English club, including scoring the winner in the semi-final against Real Madrid.
Foulkes made his debut for United in 1952 and went on to play 688 times for the club - a figure only surpassed by Charlton, Ryan Giggs and Paul Scholes.
Charlton described his old friend and colleague as "a marvellous man" and said the news of his death was "very sad".
"He was as hard as nails, as tough as teak - I was always glad I didn't have to play against him," Charlton told Press Association Sport. "He was a really, really good defensive player and you could say he helped change the course of history for United. He survived the Munich air crash and then became the captain for a time."
Foulkes, whose father and grandfather had both played rugby league for his home town St Helens, started work as a coal miner and was still going down the pit at Lea Green Colliery in the mid-1950s, by which time he was a regular member of Matt Busby's United first team and had won his only England cap, in 1954.
He played for United for his whole career, the highlight coming near the end of his playing days when he was part of the European Cup-winning team aged 36. Foulkes had played a key part in the semi-final too, scoring the winning goal against Real Madrid at the Bernabeu to secure a 4-3 aggregate win for United.
Charlton recalled: "I couldn't believe what he was doing in the Madrid penalty area in the first place, something must have been triggered in his mind, then George Best crossed it and Bill side-footed the ball into the back of the net. It was one of the most important matches in the history of Manchester United, so you could say he helped changed that history."
United are expected to wear black armbands against Bayer Leverkusen on Wednesday and to also mark Foulkes' passing at their next home match, against Everton on 4 December.
Woodward salutes a hero
The club's executive vice-chairman Ed Woodward also paid tribute to Foulkes: "Bill was a giant character in the post-war history of Manchester United. He was a very gentle man, who 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.
"Bill's contribution over almost 700 games and nearly 20 years will never be forgotten. The thoughts of everyone at the club - directors, players, staff and fans - are with Bill's family."