The Washington publication Roll Call reported a senior defense official said the Pentagon is expected to make a formal announcement Thursday.
Carl Levin, D-Mich., chairman of the Senate Armed Services Committee, said in a statement he supports the move.
"It reflects the reality of 21st century military operations," Levin said.
Sen. Kirsten Gillibrand, R-N.Y., a member of the committee, applauded the decision.
"This is a proud day for our country and the step we need to formally recognize the brave women who are already fighting and dying for our country shoulder-to-shoulder with their brothers in uniform on the front lines," she said in a statement.
The move should open about 240,000 positions across the four military branches to women, largely in infantry and special operations roles, Stars and Stripes reported.
The move, which has the backing of Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, could lead to a fully gender-integrated force by 2016, the newspaper said.
"Hip, hip, hooray!" Nancy Duff Campbell, co-president of the National Women's Law Center, said in a written statement. "Secretary Panetta's decision to lift the direct combat exclusion both opens the doors of opportunity to all women in the armed forces and eliminates the last vestige of government-sanctioned sex discrimination in the United States. Now if the best person for the job is a woman, she will no longer be barred from that job simply because of her gender."