In a rare instance of bipartisanship, the Senate passed the measure by voice vote today, just hours after the House had approved the bill the same way.
The special visa has allowed more than 12,000 Iraqi contractors, interpreters and others who aided US efforts, and their family members, to move to the United States since 2007.
It expired earlier this week, with an estimated 2,000 applications still in the bureaucratic process.
"We have a moral obligation to stand with Iraqis who stood with us during a time of war, and with this bill headed to the president tomorrow we are demonstrating that we will not abandon our Iraqi partners," said Sen. Jeanne Shaheen, a Democrat, who worked with Sen. John McCain, a Republican, on the measure.
Rep. Earl Blumenauer, a Democrat, said many translators and guides ignored their own safety to help US soldiers.
"By all accounts, thousands of these people performed critical tasks faithfully, if not flawlessly," he said in a statement. "We made an implicit promise to protect them when the American presence was scaled down, and they risked their lives to help us. Now, many are threatened on a daily basis by enemies of the United States with very long memories. We need to fulfill our promise to get them out of harm's way.