The changes have already passed in the House, and US President Barack Obama says he will sign the legislation as soon as it is received.
On Twitter, the President wrote: ''It protects civil liberties and our national security''.
In the US, the curtailing of the federal Government's sweeping surveillance of American phone records is seen as a remarkable reversal.
The passage of the measure, achieved after vigorous debate on the Senate floor, did not come without a split in the Republican ranks.
Most Democrats voted for it. For 36 hours, the National Security Agency's programme was in the dark while senators debated.
The US Government has been collecting millions of phone records in its pursuit of terrorists - not the contents of the conversations, but information about phone numbers dialled and the duration of the calls.
First disclosed by former NSA contractor Edward Snowden in 2013, the programme sparked a national debate on where the line was drawn between Americans' privacy rights and the fight against terrorism.
Mr Obama had sought reforms but kept the Bush administration programme running for nearly two days past its scheduled expiry date as Congress struggled to agree on reforms.
Under the new system, the Government will no longer be allowed to collect and store information about Americans' phone calls. If the intelligence community wants to access those records, it must get a court order and obtain the data from telephone carriers.
The change may not alter the way New Zealand monitors suspected terrorists, but a subtle alteration in the way data is collected is more than likely to follow.
During the election campaign last year, Prime Minister John Key was consistently asked about mass surveillance in New Zealand, something he declined to discuss in any detail.
Edward Snowden's statement that in his work at the NSA he regularly came across information about New Zealanders, gathered by New Zealand, was incorrect on a crucial point, Mr Key said at the time.
The Prime Minister denied New Zealand was collecting wholesale information, saying the country did not have the capability for mass surveillance.
Investigative journalist Glenn Greenwald, who visited New Zealand during the election campaign to try to lift awareness of mass surveillance in this country, dismissed assurances New Zealanders were not being spied upon by the NSA.
It was possible the NSA collected most of the data on New Zealanders, he said.
The rise of Islamic State in the Middle East has meant Australia and New Zealand have been confronting a new type of terrorism, where young men and women are being recruited from their homes here and into battles raging in Syria and Iraq.
Those young men and women are using social media to attract fellow angry or disaffected youths to the cause, in what has become an alarming trend for both countries.
In Australia, Prime Minister Tony Abbott was overruled by his Cabinet colleagues on a suggestion to remove the sole citizenship of Australians once they sign up for IS, leaving them stranded, or dead, in the battle zones.
The New Zealand Government is being challenged on similar issues of what to do with people wanting to come home after becoming disillusioned with the rigours of battle.
The US decision does open the doors for different monitoring of terror suspects among the Five Eyes nations - the US, Canada, the United Kingdom, Australia and New Zealand - and citizens may feel slightly more comfortable about security agencies having to use courts to secure data.
This is a difficult time for those five countries, not least because of the rise of radical Islam in each of the territories.
Not all Muslims are terrorists, by any stretch of the imagination.
But the ongoing movement of some young Muslims, in particular - and also some fringe elements - into acts of terror means surveillance is necessary, although it needs to be within the boundaries of what is acceptable to the general population.
