Pennsylvania is among 11 states that have not asked for a waiver, although it could apply later.
"After waiting far too long for Congress to reform No Child Left Behind, my administration is giving states the opportunity to set higher, more honest standards in exchange for more flexibility," said President Obama, who wants legislators to come up with a different approach to address the nation's educational needs.
Under No Child Left Behind (NCLB), all of the nation's public schoolchildren were supposed to be scoring proficient or higher on standardized tests by 2014. The bill, a cornerstone of the George W. Bush administration education policy, has been widely criticized for its emphasis on test performance in language arts and math, which many say has come at the expense of other subjects.
Opponents also say NCLB did not give districts and states enough freedom in how they could intervene in failing schools.
Under New Jersey's waiver proposal, the state will identify "priority" schools, the state's lowest performers, which could be subject to leadership change, other corrective action, and possibly closure. Of the schools tentatively identified, the highest concentration was in Camden.
The state also would name "focus" schools - those with low graduation rates and achievement gaps between students of different backgrounds and races that would work toward improving.
Identified as well will be "reward" schools with high proficiency or progress rates that will be recognized for their achievement.
Embracing the federal approval, Gov. Christie said Thursday: "This is not about Democrats or Republicans; it is about pursuing an agenda in the best interest of our children whose educational needs are not being met, and those who are getting a decent education but deserve a great one."