Bellamy was named on the NBA All-Star team on four occasions in his career after being selected with the number one pick in the 1961 draft.
A statement from the Hawks said: "The Atlanta Hawks family is saddened to learn of the death of Walt Bellamy at the age of 74 earlier today. The Hawks and the National Basketball Association have lost a giant.
"As an Olympic gold medalist, the first overall pick in 1961, Rookie of the Year in 1962, a four-time All-Star and a member of the Naismith Memorial Basketball Hall of Fame, his on-court accomplishments were overwhelming."
Bellamy was also a member of the US team that won gold at the 1960 Olympic Games.