Ed Husain, the foundation's co-director, claims to have been involved in a number of contentious organisations including Hizb-ut-Tahrir and the Muslim Brotherhood.
During the 1990s, he says he infiltrated British universities to recruit Muslim students into dangerous causes.
His book, The Islamist, claims that he has turned his back on extremism and began to work on reconciliation between Islam and the West.
Husain says the establishment of the Quilliam Foundation, which was named after an Englishman who converted to Islam in the 19th century, is a pivotal event.
"It's the first time since 9/11, since 7/7 [July 7, 2005 bombings in London], where there's been an effort on the part of grassroots-level Muslims, who've got a background in extremist groups themselves, to counter the al-Qaeda world view and the al-Qaeda narrative," he said.
But the new organisation has been viewed with scepticism by some Britons.
Ahmed Versi, editor of the London-based newspaper The Muslim News, said: "He [Ed Husain] is still living in the past. Things have moved on quite a bit. People have changed in the Muslim community.”
"I don't think the Quilliam Foundation knows the grassroots level movement of the Muslim community; they just don't know what's happening there."
"Their focus is on the mosque and religions and then young people. It's the same way the British government thinks. Their focus should be on the politics – both internationally and domestically, and on social issues affecting Muslims."
"They are not the middle ground," Versi said. "The majority of Muslims in this country are not from Hizb-ut-Tahrir or the Quilliam Foundation - they are in the middle of these two groups."