Mr Farage said he had “no choice” but to pick up the gauntlet thrown down by the Deputy Prime Minister as there had been no “full national debate” on the issue for many years.
But he complained that David Cameron and Ed Miliband would not be involved, urging them to take part and accusing the Prime Minister of “running” from the challenge.
“I have battled on for 20 years,” Mr Farage told LBC 97.3 radio - the same station on which Liberal Democrat leader Mr Clegg offered the debate 24 hours previously.
“I’ve been laughed at, ridiculed, attacked. But at no point in the 15 years I’ve been an MEP have we ever had a full national debate about the merits or demerits of EU membership.
“Therefore, when the Deputy Prime Minister says he wants to go public and have a debate with me on this issue, I have absolutely no choice.
“I have got to say yes because we need to have a national debate on what I think is the most important issue this country has faced for hundreds of years in terms of our constitution.
“So the answer is yes, but with one small caveat: I do really want for the Labour Party in the shape of Ed Miliband and the Conservative Party in the shape of the Prime Minister to join this debate as well.”
“Downing Street said David Cameron was too busy running the country. Well running probably is the right word,” he said of the Tory leader.
“But actually Mr Cameron, that is what the debate is about: who is running the country?”