The Warriors announced Rush's signing Tuesday.
The contract is for two years and about $2.5 million. Rush will hold the option in the second year of the deal.
Rush was Golden State's top reserve and best perimeter defender during the 2011-12 season before tearing two ligaments in his left knee in the team's 2012-13 home opener. He was traded to Utah last summer as part of a salary-shedding move.
Rush played just 38 games for the Jazz after returning from that devastating knee injury. He has averaged 8.3 points and 3.3 rebounds in six seasons.