The former party leader announced the decision simultaneously on his LBC radio show and in a column for The Daily Telegraph.
"With a heavy heart, and after all my years of devotion to the party, I am leaving Ukip today," he wrote in the newspaper.
The party has "changed fundamentally" under the leadership of Gerard Batten, Mr Farage said, accusing the MEP of an "obsession" with Robinson and a "fixation" with Islam.
"I believe he is entirely unsuitable to be involved in any political party," Mr Farage wrote of Robinson. "The fact is that his entourage includes violent criminals and ex-BNP members.
"Many Ukip members - including Ukip’s NEC – urged that Robinson should not become an advisor to Batten. Sadly, these pleas fell on deaf ears."
He added: "My heart sinks as I reflect on the idea that they may be seen by some as representative of the cause for which I have campaigned for so much of my adult life."
Robinson, whose real name is Stephen Yaxley-Lennon, is currently banned from becoming a member by party rules, but has been inciting his supporters to join Ukip so they can influence its policies.
The national executive committee (NEC) delayed a potential ballot on Robinson’s membership until after Brexit in March, but Mr Batten responded by making him an “adviser” on grooming gangs and prisons.
On Sunday, Mr Batten survived a vote of no confidence mounted by Mr Farage's supporters.
“I would never have joined Ukip as it stands today, obsessed as it is with becoming a successor to the British National Party (BNP) and the English Defence League (EDL), Suzanne Evans, Ukip's deputy chair, said as she resigned following the vote.
Ms Evans accused Mr Batten of taking Ukip in a "perverse direction" and of "putting an increasingly hostile and vicious focus on attacking the Muslim community en masse”.
Robinson founded the EDL in 2009 but left four years later. The anti-Islam activist now styles himself as an “independent reporter” and has capitalised on a surge of publicity over his imprisonment earlier this year to forge political ties across Europe, the US and Australia.
Mr Batten has appeared at several “Free Tommy” protests – including one where Batten labelled the prophet Muhammed a “paedophile” – and has repeatedly called Islam a death cult.
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