Murray, a six-year veteran, can play both guard spots. He joins Maurice Evans as free-agent additions to the backcourt after the Hawks lost sixth man Josh Childress, who stunned the team last month by signing with Greek powerhouse Olympiakos.
The 6-foot-3 Murray was released by Detroit last season before signing with Indiana. He started the final 15 games of the season at point guard for the Pacers. He averaged 11.0 points and 3.5 assists in that stretch.
"By signing Flip, it provides us with another experienced player who has the ability to play multiple positions for us," said Hawks general manager Rick Sund.
"Because of his versatility, he will be a valuable asset for us as a reserve, and we look forward to the contributions he'll bring this season," Sund said.
Terms of the deal were not announced.
Murray has averaged 9.3 points, 2.4 assists and 2.0 rebounds in his career with Milwaukee, Seattle, Cleveland, Detroit and Indiana.