Bellamy, a four-time NBA all-star and member of the United States' 1960 gold medal-winning squad, played for the Chicago Packers, Baltimore Bullets, New York Knicks, Detroit Pistons, the Hawks and New Orleans Jazz before retiring in 1975.
"The Hawks and the National Basketball Association have lost a giant," the team said in a statement. "His on-court accomplishments were overwhelming. Off the court, he was equally impactful as a family man, leader in the community, mentor and friend to many."
The 6-foot-11 North Carolina native played college ball for Indiana and was taken first overall in the 1961 NBA draft by the Packers, who subsequently moved to Baltimore.
He won Rookie of the Year honors in 1961-62 after posting averages of 31.6 points and 19 rebounds per game for the Packers.
He averaged 20.1 points, 13.7 rebounds and 2.4 assists over 1,043 career contests.
Bellamy was named to the Basketball Hall of Fame in 1993.