“The real question is what authority is left to the federal government to intervene should the states in one way or another fall short of what the hopes are?” said David Steiner, executive director of the Johns Hopkins Institute for Education Policy and a former New York state education commissioner. “We all are concerned that we not go to a place where based on where you happen to be born or which state you’re in, you face very, very increasingly different opportunities.”

The path to Wednesday’s vote was long and arduous. Even as recently as last summer, educators thought that partisan and often acrimonious bickering would stymie any movement.

No Child officially expired in 2007. As virtually every school in the country came to be labeled failing, subject to sanctions, Congress repeatedly tried to revise the law, but lawmakers could not agree on a revision. Democrats and Republicans wrangled over just what role the federal government should play in public education. Democrats wanted guarantees that the law would protect racial minorities and those from low-income families, citing its roots as a civil rights bill, initially passed in 1965 as the Elementary and Secondary Education Act. Republicans wanted states and local communities to be free to direct policies with little federal intervention.

In 2013, House Republicans passed a version of the bill that would have allowed states and districts to develop their own ways of rating schools and working with struggling ones. But Democrats flatly opposed that legislation, and Mr. Obama threatened to veto it, despite his support for changing the one-size-fits-all approach of No Child Left Behind.

For the last three years, the Obama administration has given waivers from the law’s most onerous conditions, including that every child in a school must be deemed proficient in reading and math by 2014. In its waivers, the administration added conditions that states tie performance ratings of teachers to student test scores, and that states adopt rigorous academic standards. Many states responded by adopting the Common Core, and conservatives chafed at what they saw as federal overreach.

Although the new bill requires that states take action to improve schools in the bottom 5 percent of all schools in the state as well as high schools that graduate fewer than two-thirds of students, the bill does not impose any specific action if those goals are not met.

States are required to use test scores and other academic measures to rate schools but can also include other components like student surveys. The bill specifically prevents the federal government from requiring that states evaluate teachers at all, much less use test scores to rate them, and says the education secretary cannot dictate any specific academic standards to states.