Casper, described as an underdog, was often overlooked for some of his better-known peers despite a long roster of accomplishments on the green.
He was a two-time US Open winner, including an impressive come-from-behind triumph in 1966 when he rallied from a seven-shot deficit to take the trophy.
He also won the US Open in 1959 at Winged Foot and the 1970 Masters.
From 1964 to 1970, Casper won 27 US events, six more than Palmer and Player combined.
Casper was remembered as a skilled competitor and a dedicated family man by his peers, and in 1978 he was inducted into the World Golf Hall of Fame.
"Billy Casper was one of the greatest family men -- be it inside the game of golf or out -- I have had the fortunate blessing to meet," Nicklaus said on his Facebook page.
Nicklaus said Casper often didn't get the praise he deserved.
"I think it is fair to say that Billy was probably underrated by those who didn't play against him. Those who did compete against him, knew how special he was."
The World Golf Hall of Fame hailed his putting skills and self-taught swing, describing him as "the best modern golfer who never received his due."
Casper said sports became a central part of his life as a young boy, when he was taunted for being chubby.
"It hurt, but the way I overcame it was to outrun every kid in the class. So I developed a thick skin, and athletics became my way of performing and being accepted."
Casper had suffered a series of health setbacks in recent months, including a fainting episode and a bout of pneumonia last year, ESPN reported.
Casper died at his home in Utah. The devout Mormon leaves behind 11 children, six of whom are adopted, according to ESPN.
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