WASHINGTON—President Barack Obama and Senate leaders Monday reached a New Year's budget agreement that would let income-tax rates rise for the first time in nearly 20 years, maintain unemployment benefits for millions of people and blunt the impact of spending cuts that were looming as part of the fiscal cliff.

The long-sought compromise, which will raise taxes on income over $450,000 for couples, was approved by the Senate in the early morning hours Tuesday. The House was expected to consider it later in the day.

"While neither Democrats nor Republicans got everything they wanted," Mr. Obama said in a statement, "this agreement is the right thing to do for our country and the House should pass it without delay." He said it would "grow the economy and shrink our deficits in a balanced way."

Despite concerns raised by some Senate Democrats, the bill was approved by a strong 89-8 vote, with a majority of both parties in support.

One of the most strident opponents was Democratic Sen. Tom Harkin of Iowa. Speaking on the Senate floor shortly before the vote, he declared the compromise benefited the wealthiest Americans at the expense of those who could afford it the least.