The Ukip leader was speaking as news broke the UK had voted to leave the European Union despite an on-the-day poll predicting a win for Remain.
He said: "The dawn is breaking on an independent United Kingdom!
"We have fought against the multinationals, we have fought against the big merchant banks we fought against big politics, we fought against lies, corruption and deceit.
"And today honesty, decency and belief in nation I think now is going to win.
"And we will have done it without having to fight, without a single bullet being fired.
"We will have done it by damn hard work on the ground, by people like my friend Mr [bankroller Arron] Banks here. And by people in the Labour party and the Conservative Party and of Ukip and no party.
"I hope this victory brings down this failed project and leads us to a Europe of sovereign states."
Jo Cox was shot and killed last Thursday in Birstall, near Leeds.
The attack came on the steps of the town library just before 1pm, where the 41-year-old mother-of-two had been holding a surgery with her constituents.
The Brexit vote will not only likely cause political chaos in the EU, but calls into question the very future of the UK as a united country.
SNP leader Nicola Sturgeon has said that the Brexit vote “makes clear that the people of Scotland see their future as part of the European Union” - hinting she will push for a second Scottish independence referendum.