The move ends an embarrassing episode for the administration, which repeatedly miscalculated the needs of veterans and used outdated budget models when fashioning estimates for Congress.
The funds, which close a gap for the current budget year, were added to a $26.3 billion bill for next year's budget for the Interior Department.
The underlying budget bill generally fits within Mr. Bush's budget outlines as it cuts almost $700 million from current levels. But when Congress returns from its summer recess in September, lawmakers are sure to test the president's resolve to cut almost 1 percent from domestic agencies whose budgets Congress funds each year.
The Senate also cleared a $3.8 billion measure funding Congress' own budget.
The extra veterans funds were needed after the Veterans Affairs Department underestimated the number of veterans who would seek care as well as increased costs of treatment and long-term care.
Initially, the VA said it faced about a $1 billion shortfall that could be managed by tapping reserve funds and its budget for infrastructure improvements. That did not fly with lawmakers, who insisted on adding emergency funds on top of the $28 billion appropriated last year for veterans' medical needs.