Senate Democratic leaders said they planned to follow suit with similar legislation and send a bill to George Bush, the US president, as soon as possible.
The FBI is now going to investigate the incident on September 16, taking control from the state department as soon as a full team has been assembled in the Iraqi capital.
Sean McCormack, the state department spokesman, said that the step did not imply that the investigation would result in criminal charges being brought.
Under the state department's contract with Blackwater, the company's guards would have provided security for the FBI team while in Iraq.
John Miller, an FBI spokesman, said the team will rely on US government personnel "to avoid even the appearance of any conflict" of interest.
The present law, called the Military Extraterritorial Jurisdiction Act, covers personnel supporting defence department operations overseas, but not those working for the state department. Blackwater's primary mission is to protect state department officials, so defence lawyers are expected to argue that the law does not apply to them.
At the same time, all US contractors are immune from prosecution by Iraqi courts.
White House reaction
The White House and congressional Republicans said they support the intent of the bill, but thought it was drafted poorly.
In a statement issued on Wednesday, the White House said the bill would have "unintended and intolerable consequences for crucial and necessary national security activities and operations". The statement did not explain further or give examples on how the bill would affect national security.
The White House referred questions to the justice department, which declined to comment.
Prior to passage, the House voted 342-75 to ensure the legislation would not affect intelligence operations.