Hamilton played college basketball for the Iowa State Cyclones from 2008 to 2010 under Greg McDermott, and Louisiana State University during the 2011–12 season under Trent Johnson after being required to redshirt the 2010–11 season due to NCAA transfer requirements.
In August 2012, Hamilton signed with KK Cibona and has expressed a desire to play for the Croatian national basketball team.  In January 2013, he moved to VEF Rīga after an agreement with Cibona allowed him to switch clubs.  He left the team in May.
On March 14, 2014, he signed with the Miami Heat for the rest of the season.  On March 20, 2014, he was assigned to the Sioux Falls Skyforce.  On March 24, 2014, he was recalled by the Heat. The Heat made the 2014 NBA Finals, where they lost to the San Antonio Spurs in five games. Hamilton did not play a game in the 2014 playoffs for Miami.
On February 19, 2015, Hamilton was traded to the New Orleans Pelicans in a three-team trade involving the Phoenix Suns.  On March 3, 2015, he was waived by the Pelicans before appearing in a game for them.  Two days later, he was claimed off waivers by the Minnesota Timberwolves. 
On July 27, 2015, Hamilton signed a one-year deal with Valencia of the Liga ACB and the Eurocup.  Valencia reached the league's semi-finals and Hamilton earned All-Liga ACB First Team honours as the top power forward in the league.
On July 11, 2016, Hamilton signed a multi-year contract with the Brooklyn Nets.  He made his debut for the Nets in their season opener on October 26, 2016 against the Boston Celtics. In 25 minutes off the bench, he recorded a career-high 19 points and 10 rebounds in a 122–117 loss.  On December 20, 2016, he grabbed a career-high 11 rebounds in a 116–104 loss to the Toronto Raptors. 
On July 13, 2017, Hamilton was traded to the Toronto Raptors in exchange for DeMarre Carroll, a future first-round pick and a future second-round pick.  The following day, however, he was waived by the Raptors. 
NBA career statistics
|GP||Games played||GS||Games started||MPG||Minutes per game|
|FG%||Field goal percentage||3P%||3-point field goal percentage||FT%||Free throw percentage|
|RPG||Rebounds per game||APG||Assists per game||SPG||Steals per game|
|BPG||Blocks per game||PPG||Points per game||Bold||Career high|