Mr Farage made the announcement on his LBC show on Tuesday. "It's done," he said.
Mr Farage, who had three different stints as Ukip leader, said: "Over the course of the last few months, under this leader, he seems to be pretty obsessed with Islam. Ukip wasn't founded to be a party based on fighting a religious crusade.
"He's also obsessed with this figure called Tommy Robinson, who is seen by some to be a great hero standing up and fighting for working class people, but who has a pretty suspect record - and who brings with him a group of people amongst which we see scuffles, violence. Many have criminal records, some pretty serious.
"All of it has been dragging Ukip away from an electoral party into a party of street activism. I have warned this direction was catastrophic, particularly at the time when the great Brexit betrayal is upon us. Both the Labour and Conservative parties have broken promises that were made not just in the referendum but in the general election as well."
Mr Farage, who last month launched a coup against Mr Batten over his appointment of Mr Robinson as an advisor on rape gangs and prison reform, continued: "Things couldn't be better for Ukip, but unfortunately we've gone in this direction of street activism and turning a blind eye to extremist politics.
"There was one last hope that the party's national executive at the weekend would do something about this and pass a motion of no confidence in Gerard Batten." Mr Batten survived the vote.
On Sunday, protesters are set to march through central London for a pro-Brexit march organised by Ukip and backed by former English Defence League leader Mr Robinson, real name Stephen Yaxley-Lennon.
Mr Farage said: "The image that will give of what Brexit stands for is something that our enemies will use against us for perhaps many years to come.
"Damaging Ukip is one thing, damaging the Brexit cause is even worse, and I, with a very heavy heart - given how much I cared for this party and the people in it - have reached a very sad decision that I simply can't go on with it.
"I don't recognise the party as being the one I helped to found and fought for. I believe the brand has been so damaged that it's not able to pick up the political opportunity that's there staring it in the face. As of now, I am no longer a member of Ukip... it's done."
Responding to the announcement, Mr Batten tweeted: "I hear that Nigel Farage has resigned from UKIP.
"Nigel & I were founder members of UKIP in 1993. I have always given him full credit for his work in UKIP bringing about and winning the Referendum. However, I feel that he left UKIP in spirit after the Referendum."