The bill represents the latest step in fulfilling a January promise by President Barack Obama to end the NSA's collection of domestic calling records. If enacted, it would represent the most significant change to come in the wake of the leaks of once-secret surveillance programs by former NSA systems administrator Edward Snowden.
The measure was co-sponsored by Republicans, including Sen. Ted Cruz of Texas.
It would not affect most NSA surveillance, which operates under different authorities than the Patriot Act provision under which the agency was collecting telephone calling records.
"This is an historic opportunity, and I am grateful that the bill has the support of the administration, a wide range of privacy and civil liberties groups, and the technology industry," said Leahy, D-Vermont, judiciary committee chairman.
Leahy's bill drew praise from the American Civil Liberties Association and other activist groups because it tightened a provision they criticized in a similar bill that passed the House in May. The House bill included a vaguely worded definition that some believed continued to allow bulk collection of American records, something the bills are designed to curb.
Both bills allow the NSA to request the U.S. calling data from the phone companies in terrorism investigations after a secret order of the Foreign Intelligence Surveillance Court. The difference is that it will be the companies, not the NSA, holding the records.
"While this bill is not perfect, it is the beginning of the real NSA reform that the public has been craving since the Patriot Act became law in 2001," said Laura Murphy, director of the ACLU's Washington Legislative Office.
Cruz said, "Republicans and Democrats are showing America that the government can respect the privacy rights of law-abiding citizens, while at the same time, giving law enforcement the tools needed to target terrorists."