The NSA was allowed to collect this information without a warrant thanks to a US law passed in 2008.
In a statement it said that an internal review had revealed several problems with the spying programme and its effect on US citizens' privacy.
Surveillance experts said the NSA's decision was "very significant".
The NSA is not allowed to conduct surveillance within the US but it managed to skirt this restriction thanks to one section of the 2008 Foreign Intelligence Surveillance Act (Fisa).
This let it grab the phone calls and messages of US citizens which mentioned or otherwise involved people outside the US it was keeping an eye on.
The NSA had been widely criticised because using Fisa had meant it had scooped up lots of messages, texts and other material sent by Americans without having to apply for a warrant.
In its statement, the NSA said technical limits, privacy problems and the difficulty of carrying out this type of surveillance had driven its decision. It also said it would delete the "vast majority" of data collected via this spying programme.
The powers to spy outlined in Fisa were due to be scrutinised this year by the US Congress and are set to be renewed by the end of 2017. Many members of Congress have been critical of the spying effort and politicians were expected to significantly limit its scope during the renewal and review process.
The Fisa spying programme has also been criticised by the US Federal Intelligence Surveillance Court, which oversees NSA requests for surveillance warrants.
The NSA had defended the Fisa-allowed spying, saying that it had helped it gather "critical" intelligence.
Julian Sanchez, a privacy and surveillance expert with the Cato Institute, said the broad reach of Fisa-sanctioned spying had made it a key target of civil liberties campaigners.
"Usually you identify a specific individual to scrutinise their content; this was scrutinizing everyone's content to find mentions of an individual," Mr Sanchez told Reuters.

The 23-year-old joined Livingston on a deal until the end of 2015-16 after leaving Dundee United in January.
He previously spent the first part of last season on loan at Almondvale Stadium, and made a total of 30 appearances for Livi last term.
McCallum, who has also played for Arbroath and Berwick, is the League Two side's 14th signing of the summer.
Find all the latest football transfers on our dedicated page.

Their lab-based work suggests there is a biological step that can restore normality and stop cells replicating out of control.
When the US researchers added molecules called microRNAs, it put the brakes on cancer, Nature Cell Biology reports.
Although the early tests in a dish look promising, it is unclear whether it will help treat people with cancer.
The Mayo Clinic researchers are hopeful that the new mechanism they have found could apply to all types of cancer.
It brings together two strands of science - cell adhesion and microRNA (miRNA) biology - that, until now, had not been linked.
Scientists had thought adhesion molecules were simply the glue that holds cells together. But then others found they might have signalling roles.
The Mayo Clinic work shows adhesion molecules connect cells and signal via miRNAs to control cell growth.
If this becomes deregulated it can drive cancer.
But replenishing cells with miRNAs can remedy this.
Lead researcher Dr Panos Anastasiadis said: "By administering the affected miRNAs in cancer cells to restore their normal levels, we should be able to re-establish the brakes and restore normal cell function.
"Initial experiments in some aggressive types of cancer are indeed very promising."
Henry Scowcroft, Cancer Research UK's senior science information manager, said: "This important study solves a long-standing biological mystery, but we mustn't get ahead of ourselves.
"There's a long way to go before we know whether these findings, in cells grown in a laboratory, will help treat people with cancer. But it's a significant step forward in understanding how certain cells in our body know when to grow, and when to stop. Understanding these key concepts is crucial to help continue the encouraging progress against cancer we've seen in recent years."
The US National Security Agency (NSA) is to end surveillance on messages sent by US citizens that mention foreign intelligence targets.
[NEXT_CONCEPT]
Plymouth Argyle have signed former Livingston goalkeeper Marc McCallum on an undisclosed-length contract.
[NEXT_CONCEPT]
Scientists believe they may have found a way to turn cancerous cells back into healthy tissue.