"I would like to extend our deepest condolences to Nat's family, who are very much in our thoughts at this time," added Gartside in a statement on the Bolton website.
"We will miss him but we will celebrate his life, his legacy and great times that he brought to Bolton."
Manchester United legend Sir Bobby Charlton led the tributes to one of the sport's true greats.
"The first time I saw a professional game was at Newcastle and Nat Lofthouse was playing," Charlton told BBC Radio 5 live's Sportsweek programme. "They were talking about him as this youngster that had just burst on to the scene and he was fantastic.
"He was a leader, he had fantastic ability in the air and he was strong. He was a talisman.
"I played about four of five games with him with England at the end of his career and I felt that he was the one that was in charge.
"I know a lot of people in the game of football will be very, very sad today about Nat Lofthouse, who was a great player without any question.
"You just put the ball in there at any height and he was so brave. He scored phenomenal goals in the air.
"In those days, if you were a centre forward, you had to do more than score goals. You had to lead. You had to be tough.
"It was a hard game then. It wasn't like today, it was so tough. The pitches were bad, the ball was heavy, the equipment was awful but Nat Lofthouse loved the game of football. He was ever so proud to be a part of it."
Ex-West Brom and Arsenal player Don Howe, who was an England team-mate of Lofthouse, also told Sportsweek: "He was not only a great player, he was a great character.
"On the pitch - wonderful, powerful, put the ball in the box and he will do the job for you.
"Off the pitch, I was one of the young caps then, he would come up to you and say 'hello son, how are you doing?' He would give you a real gee up, that's how he was.
"I was one of the young lads of the group then and wherever he was in the hotel, he would be around everybody picking people up. He spent his time geeing up some of the players."
Lofthouse captained Bolton in two FA Cup finals, the first time in 1953 when he came up against Sir Stanley Matthews, when the Trotters were memorably beaten 4-3 by Lancashire rivals Blackpool at Wembley.
Five years later, Lofthouse won a winner's medal after scoring both goals in the 2-0 win over Manchester United, only three months after the Old Trafford club had been involved in the Munich air disaster.
Lofthouse, who was footballer of the year in 1953, scored a total of 255 league goals as well as 30 goals in domestic cup competition.
"He went on to become the definite one-club man and epitomised the traditional English centre-forward," said BBC Radio 5 live chief football correspondent Mike Ingham. "He was the Alan Shearer of his day."
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