Now committees will try to reconcile the two bills for final passage.
The bill would allow more contracting with private health providers to reduce the long waits for veterans.
U.S. Senator Jeff Merkley says Congress failed to pass similar measures last year, but these scandals got many politicians on board.
"One thing the V-A is doing a good job on is reducing the backlog of veterans applying for benefits. Because if veterans are waiting for approval for several years, that's several years they are not getting the benefits they should. So we need to keep pushing forward on that. And once they are approved for benefits, they need to get through the door to see appropriate health care professionals to get their appointments."
It's estimated, allowing veterans access to private medical care could increase spending for V-A care by 35 billion over the next ten years.