The Lakers made the moves Saturday, a day after a loss to Sacramento dropped them to 0-5 in the preseason.
Nelson played parts of three seasons at UCLA, making the all-conference first team in 2011 as the Bruins' leading scorer and rebounder. But UCLA coach Ben Howland dismissed Nelson from the team in December 2011 following a series of suspensions and benchings.
Nelson played briefly in Lithuania before going unselected in last June's NBA Draft. He played on the Lakers' summer league team and earned an invitation to training camp.