The Indianapolis Star first reported the deal. Mark Bartelstein, the agent for both players, confirmed the move on Sunday.
Rush averaged 8.9 points and 3.6 rebounds in three seasons for the Pacers. The Pacers considered him a part of the core group of young players, but the team eventually added enough talent at his position to make him expendable.
Rush showed great potential at times, but also found trouble. He was suspended for five games last season for violating the league's substance abuse policy.
Amundson has averaged 4.1 points and 3.7 rebounds in five seasons, primarily with Philadelphia, Phoenix and Golden State. He shoots 52 percent from the field for his career.