WASHINGTON — The Senate approved a sweeping new farm bill on Thursday that would cost nearly $1 trillion over the next 10 years, financing dozens of price support and crop insurance programs for farmers and food assistance for low-income families.

The bill passed with overwhelming bipartisan support, 64 to 35. It now goes to the House, where it faces a much tougher road because conservative lawmakers want to make deeper cuts in the food stamp program, which serves about 45 million Americans. “This bill represents significant reform,” said Senator Debbie Stabenow, Democrat of Michigan and chairwoman of the Senate Agriculture Committee. “It cuts subsidies, it cuts the deficit and it creates jobs.”

Senator Pat Roberts, Republican of Kansas and the ranking member on the committee, called the legislation the best bill possible. “It shows what can happen if we break the logjam of partisanship and work together to get something done,” Mr. Roberts said.

Although the bill is known as the farm bill, the majority of the spending, about $80 billion a year, goes to the food stamp program. The Senate bill would cut a total of $23.6 billion from current spending levels, including about $4.5 billion from food stamps, but senators rejected several proposals that would have made even deeper cuts.