The anti-hate campaigners crowdsourced funding to sue the former Ukip leader for libel over the claims, and demanded £100,000 in damages.
Mr Farage has reportedly now agreed to withdraw his statement and not repeat it.
The comments in question were made during an LBC radio show last December. Mr Farage was responding to Brendan Cox, the husband of murdered Labour MP Jo Cox, who had accused the 53-year-old MEP of stoking tensions over a terrorist attack on a Berlin Christmas market. Mr Farage had appeared to blame the attack on Angela Merkel, leading Mr Cox to claim he was "blaming politicians for the actions of extremists".
In response, Mr Farage said: "Yes, well of course he would know more about extremists than me, Mr Cox. He backs organisations like Hope Not Hate, who masquerade as being lovely and peaceful, but actually pursue violent and undemocratic means.”
After Mr Farage refused to retract the allegation, Hope Not Hate launched an appeal asking the public to help fund a legal case. It said 16,000 people have since donated to the fund.
Facing the threat of a court battle, Mr Farage has now agreed to withdraw his claims.
In a statement filed to the court, he reportedly said: "Having now considered the position further I am happy to acknowledge that Hope Not Hate does not tolerate or pursue violent or undemocratic behaviour."
The MEP also agreed not to repeat the claims or allow anyone to do so on his behalf.
Nick Lowles, Hope Not Hate's chief executive, said: "I am delighted with this victory and that we've held Nigel Farage to account.
"The case was about the truth and about HOPE not hate saying no to Nigel Farage's attempts to smear us. For too long right-wing politicians have got away with smearing and abusing their opponents. We drew a line in the sand and ‘no more'.
"We are an avowedly peaceful organisation and Farage's false claims were deeply damaging to the vital work we do bringing communities together across cultural and religious divides.
"Anyone else repeating these smears our pursuing a false news agenda against our organisation should be put on note that we won't hesitate to take further action to protect our reputation. We also hope this case sends a wider signal to right-wing politicians that smearing people will no longer be accepted."
Mr Farage said: “I am very surprised at Hope Not Hate’s announcement today that they have won their legal case against me. Some victory! Their statement today is thoroughly disingenuous."
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