The House vote passed 260-167 and helped close out sometimes quarrelsome negotiations between the Obama administration and Republicans dominating the House.
The Senate voted 81-19 to pass the budget.
The legislation drew support from lawmakers in both parties, but little if any enthusiasm.
The president has said he'll sign it into law.
The bill cuts community health programs, grants for state and local police departments, the Environmental Protection Agency and community development grants.
In February, Republicans muscled through a plan that called for $60 billion-plus in cuts. The current plan is considerably less, but GOP officials said it reverses the ever-upward course of spending.
"It stops the bleeding. It halts the spending binge and starts us moving us back in the right direction," Boehner said. "Does it cut enough? No. Do I wish it cut more? Absolutely."
Some Republicans have expressed concern since learning that the bill would cut less than $1 billion from this year's deficit, but Boehner preferred to focus on the long-term implications of the measure - and a vote Friday on a 10-year GOP budget blueprint that promises $6.2 trillion in savings below Obama's February budget.
The 2011 spending measure produces its $38 billion in cuts by including nearly $18 billion in changes to benefit programs like children's health care, highway funding and a fund for crime victims. Many of those cuts, however, would have little to no impact on the deficit.
Later Thursday, the GOP-dominated House will kick off debate on its long-term budget plan, a measure promising stiff cuts to domestic agency budgets that total $1.8 trillion over 10 years.
The GOP measure, a non-binding blueprint that sets a theoretical framework for future legislation, would also sharply cut Medicaid and transform it into a block grant program operated by the states. It doesn't touch Social Security, however, or immediately cut Medicare.
The Associated Press contributed to this report.