WASHINGTON — With his signature today, President Barack Obama is setting the nation’s public schools on a sweeping new course of accountability that will change the way teachers are evaluated and how the poorest performing schools are pushed to improve.

Obama will sign a bipartisan bill that easily passed the Senate Wednesday and the House last week — long-awaited legislation that would replace the landmark No Child Left Behind education law of 2002, now widely viewed as unworkable and overreaching.

One key feature of No Child remains: Students will still take the federally required statewide reading and math exams. But the new law encourages states to limit the time students spend on testing and diminishes the high stakes for underperforming schools.

By turning more decision-making powers back to the states, the law would end more than a decade of what critics have derided as one-size-fits-all federal policies dictating accountability and improvement for the nation’s 100,000 or so public schools.

Republican Sen. Lamar Alexander of Tennessee, who leads the Senate Education Committee, called the legislation a “Christmas present” for 50 million children across the country. Alexander was a chief author of the bill along with Democratic Sen. Patty Murray of Washington — and in the House, Education Committee Chairman John Kline, R-Minn., and ranking Democrat Bobby Scott of Virginia.

“You’ll see states taking the opportunity to serve kids better, meaning it’s not just a conversation about labeling schools but also a conversation about when a school’s not doing right by kids,” Chris Minnich, executive director of the Council of Chief State School Officers, said in an interview.

The new law gives states flexibility, beyond using testing results, to consider additional performance measures such as graduation rates.