Bellamy chose to play basketball at Indiana University. "In the summer after my junior year of high school I played with some guys from Indiana", he said. "Indiana at the time was the closest school to the South that would accept African-Americans. It was an easy transition for me to make. Not that I was naive to what was going on in Bloomington in terms of the times, but it didn't translate to the athletic department or the classroom. Every relationship was good."

Bellamy graduated from Indiana University with the most school rebounds in a career with 1,087 in only 70 games (15.5 per game). He also averaged 20.6 points per game and shot 51.7 percent from the floor for his college career. As a senior, Bellamy averaged 17.8 rebounds per game (still Indiana's record). He also holds the school records for most rebounds in a season (649) and most double-doubles in a career (59). In 2000, he was selected to Indiana University's All-Century Team.

In his final college game, he set Indiana and Big Ten Conference records that still stand with 33 rebounds (and 28 points) in an 82-67 win over Michigan. Bellamy was named an All-American in both his junior and senior year (1960 and 1961). Bellamy was the first Hoosier taken No. 1 in the NBA draft and the first Hoosier named NBA Rookie of the Year.

Bellamy was the starting center on the gold medal-winning American basketball team at the 1960 Summer Olympics. 10 of the 12 college players on the undefeated American squad went on to play professionally in the NBA, including fellow Big Ten player Terry Dischinger and fellow future Hall-of-Famers Jerry West, Oscar Robertson, and Jerry Lucas.

Bellamy had a stellar 14-year career in the NBA, and was the NBA first overall draft pick in 1961. Bellamy was named the NBA Rookie of the Year in 1962 after having arguably one of the three greatest rookie seasons in NBA history (along with Wilt Chamberlain and Oscar Robertson). His 31.6 points per game average that season is second all-time for a rookie to Wilt Chamberlain's 37.6, and the 19 rebounds per game he averaged that season is the third-best all-time rookie mark (to Chamberlain's 27 and Bill Russell's 19.6). No NBA rookie has since surpassed Bellamy's 973 field goals during the 1961-62 season.

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