The agreement clears the way for the Senate and House of Representatives to debate and vote on the measure next week.
Bush's initial proposal for the legislation had faced opposition from some Republican senators, who said they feared it would have allowed abusive treatment of detainees and undermined protection extended by the Geneva Convention.
Bush welcomed the agreement, saying the new legislation will give the CIA, the Central Intelligence Agency, the ability to continue interrogations of terror suspects and protect America from possible attacks.
The agreement has been criticized by a leading U.S. rights group, the American Civil Liberties Union, which said it fails to uphold the United States' obligations under international treaty. The group urged lawmakers to reject the bill.
(compiled from agency reports)