Under the deal, the states must show they will prepare children for college and careers, set new targets for improving achievement among all students, reward the best performing schools and focus help on the ones doing the worst.
Obama has called former President George W. Bush's most hyped domestic accomplishment an admirable but flawed effort that hurt students instead of helping them. Republicans have charged Obama is overreaching his authority by granting waivers and is imposing his vision for education on states.
"This plan does not constitute the long-term reform families, schools, and students need. It's a temporary Band-Aid on a problem that must be resolved through legislation," said Rep. John Kline, R-Minn., chairman of the U.S. House Education and the Workforce Committee.
States have been asking for relief from the law as the 2014 deadline neared.
"The waiver lets New York move away from NCLB requirements that were unproductive or unrealistic," state Education Commissioner John B. King said in a prepared statement. "We're making a new set of promises to our students. Now we have to live up to those promises."
Duncan said the Obama administration prefers that Congress fix the law but insisted students can't wait for that. In an election year in a divided Congress, that appears unlikely to happen.
Associated Press writers Stephen Singer and Michael Melia in Hartford, Conn., and Carolyn Thompson in Buffalo, N.Y., contributed to this report.