The move allows Senator Dianne Feinstein, the powerful chair of the Intelligence Committee, to send the 400-page executive summary as well as key conclusions and recommendations to the White House for review.
Senator Saxby Chambliss, the committee's top Republican, said he opposed the exhaustive investigation in the first place, but reluctantly voted to declassify parts of it so that the American people can assess the program's legacy for themselves.
"We need to get this behind us," Chambliss told reporters.
Feinstein said she hoped the redactions would be "as few as possible," and that she believed the process would take at least a month.
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She said it was important to expose the brutal interrogation program, which she described as "a stain on our history."
"This nation admits its errors, as painful as it may be," she added.
The program, begun shortly after the 9/11 attacks of 2001 and eventually shut down by Obama, used "enhanced interrogation techniques" including waterboarding, which Obama and some lawmakers have likened to torture.
The report caused a rift between the intelligence community and the Senate panel, which often cooperates closely with the Central Intelligence Agency and other spy departments.