Saudi Arabia has criticized the bill, which was passed by a voice vote in the Senate in May. President Obama is expected to veto the measure, known as the Justice Against Sponsors of Terrorism Act.
News of the House vote was first reported by Politico.
The proposal, from Sens. Chuck Schumer, D-New York, and John Cornyn, R-Texas, would give families of 9/11 victims the ability to sue Saudi Arabia for any alleged role in the 2001 terror attacks.
In July, the intelligence community released the classified 28 pages of Congress' first investigation in the Sept. 11 attacks. The information in the pages lays out a number of circumstances that suggest it's possible two of the 9/11 hijackers living in California had been receiving operational support from individuals loyal to Saudi Arabia in the months leading up to the attacks.
Intelligence officials say the information was preliminary and was further investigated in later 9/11 investigations.