Rush averaged 9.1 points over 67 games in 2010-11. He spent three seasons with the Pacers after being acquired in July 2008 from Portland, which selected him with the 13th overall pick of the 2008 draft.
"I want to thank Brandon for his three seasons with us," said Pacers president of basketball operations Larry Bird in a statement. "Any time you make a trade, especially when it's a guy such as Brandon who you've come to know and like, it's tough, but he'll get a good opportunity and a fresh start with Golden State."
In 224 games with the Pacers, Rush averaged 8.9 points with 3.6 rebounds.
Amundson saw action in 46 games in 2010-11, tallying 4.3 points and 4.0 rebounds per contest.
"We're very happy to get Lou," Bird added. "He gives us another big guy who rebounds and plays extremely hard. He gives us more depth up front and will be a player who gives us energy off the bench."
A five-year undrafted veteran out of UNLV, the well-traveled Amundson has played for Utah, Philadelphia, Phoenix and Golden State.