Hamm is the son of Sandy and Cecily Hamm. In addition to his twin brother, Paul Hamm, his older sister, Elizabeth (Betsy), is a former member of USA Gymnastics Senior National Team. She competed for the University of Florida, where she became the NCAA’s national balance beam champion in 1998 and was a seven-time All American. His father was an All-American springboard diver.
He competed at the 2000 Olympics in Sydney while aged 17, and the 2004 Summer Olympics in Athens, alongside his twin brother Paul, helping the American team win the silver medal in the team gymnastics competition. Morgan's contribution to this victory was vital as he performed on four of the six pieces and was the highest scorer for the team on vault and high bar. He also competed in floor and high bar finals, and only a tie-breaker kept him from taking bronze on the latter event. Morgan was a member of the US team at the 2003 World Championships, where he helped earn a silver medal.
In February 2007, Hamm announced that he would return to competitive gymnastics. He competed at the 2007 Visa National Championships, on floor and pommel horse. He competed at the 2008 Nationals and at the Olympic Trials. He was warned by the United States Anti-Doping Agency in July for testing positive for glucocorticosteroid, which is not performance-enhancing or banned but only allowed if proper paperwork is filed to document that the drug is used for therapeutic reasons. Hamm received the substance through an anti-inflammatory shot to his injured ankle but failed to file the paperwork and his results at the May 24 nationals competition were thrown out. Hamm claimed that he had a legitimate medical need for the drug. He was ultimately selected for the 2008 Olympic team. However, Hamm withdrew from the games on August 7, 2008, due to an ankle injury.Alexander Artemev replaced him on the team.
Morgan Hamm also competed alongside his brother, Paul Hamm, in the two 2005 Sasuke competitions (#14, #15,). In the 14th competition he timed out before he could attempt the "Rope Climb" in the First Stage. In the 15th competition, he made it to the third stage and ultimately failed on the "Curtain Cling" obstacle. Unlike his brother, he did not compete in the 16th competition.