Beamon was born on Aug. 29, 1946, on Long Island, N.Y. His natural father died before his birth, and his mother died of tuberculosis before he reached his first birthday. He was raised by his stepfather and his grandmother. Growing up, Beamon spent time in reform school before finding his niche as an athlete at Jamaica High School. In 1965, he set a national high school triple jump record of 50 feet, 3³/₄ inches (15.34 meters). His great leaping ability also made him an excellent basketball player.

Beamon earned an athletic scholarship to North Carolina Agricultural and Technical State University but later transferred to the University of Texas at El Paso. While still a student, he earned a silver medal in the long jump at the Pan-American Games and won both the long jump and triple jump crowns at the 1968 National Collegiate Athletic Association championships. Despite his success, Beamon lost his scholarship when he and seven teammates boycotted a track and field meet against Brigham Young University to protest the Mormons' opinions on race; university officials ruled that participants in the boycott voluntarily removed themselves from the team.

Although there was a movement among African American athletes to boycott the 1968 Summer Olympic Games in Mexico to protest American racism, Beamon decided to compete. Aided by Mexico City's thin air, Beamon made a jump of 29 feet, 2¹/₂ inches (8.90 meters) to win the gold medal. His record stood until 1991, when Mike Powell made a jump of 29 feet, 4¹/₂ inches (8.95 meters) at the world championships in Tokyo, Japan.

Plagued by a hip injury, Beamon never jumped more than 27 feet (8.2 meters) after the Mexico City games, and he retired before the 1972 Olympics. He received a bachelor's degree in sociology and physical education from Adelphi University, where he also played basketball. He went on to earn a master's degree in psychology and counseling from San Diego State University and operated a youth center for children of the ghetto. He also coached track and field and helped the United States Olympic Committee with fundraising. Beamon was inducted into the National Track and Field Hall of Fame in 1977, and he entered the United States Olympic Hall of Fame in 1983.