The bill was passed 221-107, with no Democrats supporting it and 12 Republicans voting against it.
It returns decisions back to the states on how to deal with failing schools, how and when to evaluate teachers and how to spend federal money to educate poor, disabled and non-English-speaking students.
The bill marks a turn away from the 2002 law that set goals for academic achievement and penalties for schools falling short, The Washington Post said.
"States and schools have been clamoring, clamoring for less federal mandates," said the lead sponsor of the bill, Rep. John Kline, R-Minn. "We should not tie the hands of teachers and school officials."
The legislation faces an uncertain future. President Barack Obama has threatened to veto it, and Senate Democrats are preparing a version that retains much of the federal oversight of public education, the newspaper noted.
Notable deaths of 2014 [PHOTOS]