He said in a statement that he acknowledged "the dangers of far-right extremism and the ongoing need to counter Islamist ideology not with violence but with better, democratic ideas."
And he distanced himself from the behavior of some EDL supporters, telling the BBC that "whilst I want to lead a revolution against Islamist ideology, I don't want to lead a revolution against Muslims."
He said that as the face of the EDL, he was tired of being associated with the group's excesses such as the supporter photographed sporting a tattoo of an exploding mosque.
"When some moron lifts up his top and he's got the picture of a mosque saying 'boom' and it's all over the national newspapers it's me," he said.
"It's when I pick up my kids from school the parents are looking at me, judging me on that. And that's not what I've stood for and my decision to do this is to be true to what I stand for."
Quilliam co-founder Maajid Nawaz said the announcement was "a very proud moment" for his group.
"We have been able to show that Britain stands together against extremism regardless of political views and hope to continue supporting Tommy and Kevin in their journey to counter Islamism and neo-Nazi extremism," he said.
But Mohammed Shafiq, chief executive of Muslim think-tank the Ramadhan Foundation, said Robinson and Carroll should explicitly renounce "their fascist views on Islam and Muslims."