The UK would still be able to trade freely within Europe even if it left the EU, Michael Gove has said.
The justice secretary said the UK could be part of Europe's free trade area to avoid trade tariffs, even if it was not a member of the EU single market.
The pro-Leave campaigner also said a UK exit would lead to the "democratic liberation of a whole continent".
The Remain camp said his statements "don't bear proper scrutiny" and would put British jobs at risk.
Mr Gove used a speech in London to set out his vision of what the country would look like in the event of a vote to leave the EU on 23 June.
On trading, he said the UK would be part of the European free trade zone with access to the European single market but "free from EU regulation which costs us billions of pounds a year".
He said the UK would also be able to arrange trade deals with countries including the US, China and India.
It follows Treasury forecasts that an exit from the EU could see the economy 6% smaller by 2030 - costing households the equivalent of 4,300 a year.
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The Leave campaign has been branded "Project Fantasy" by its opponents for its alleged lack of economic clarity but Mr Gove hit back, and accused opponents of "wanting us to believe that Britain is broken and beaten".
He said the idea Britain outside the EU would "instantly become some sort of hermit kingdom" was a "fantasy" and treated voters "like mere children, capable of being frightened into obedience by conjuring up new bogeymen every night".
Analysis by Laura Kuenssberg, BBC political editor
For weeks politicians who want to persuade you to leave the EU have been under fire from the other side for not being clear on their vision of the economy. Today one of the leaders of the Vote Leave campaign sketched in some, but not all, of the answers.
So, what do we know now that we didn't know when we got up this morning? There is a bit more clarity about the campaign's broad approach. This is what they claim.
- Britain would be able to trade in the European Free Trade Zone that stretches from Iceland to Turkey - this includes countries like Bosnia, Serbia and Albania
- They want access to trade with the rest of the EU, but would not try to keep Britain inside the single market, the EU's trading territory where goods, services and people can move freely across the continent
- Britain would not be subject to EU law
- Britain would not have to accept the EU rules on freedom of movement where citizens from the 27 other countries can freely move to live and work in the UK.
That is quite a list of claims. Read more from Laura
The justice secretary said a vote to leave would be a "galvanising, liberating, empowering moment of patriotic renewal".
It would enable the UK to "take back control" - of its sovereignty, economy, borders and spending priorities, he said.
He said a number of analysts had said there would be "long term benefits" to the economy of leaving.
And he suggested a vote to stay in the EU would effectively maroon the UK within the EU, where it would have to accept further political and financial integration.
He likened a vote to stay in the EU as a vote "to be a hostage, locked in the boot of a car driven by others to a place and at a pace that we have no control over".
He also said the UK's rebate would be "whittled away" and more powers would have to be ceded to the EU in areas such as tax and asylum.
Mr Gove claimed the European Court of Justice had undermined the UK's security, saying it had control over the way the country applies asylum rules and monitors and deports terrorism suspects.
The approach taken by EU leaders "could not and will not survive" a UK vote to leave which would "strengthen and liberate" those across the EU fighting for powers to be returned, he said.
But former Conservative Attorney General Dominic Grieve told the BBC's Radio 4 Today that Mr Gove's arguments were "unfounded and untenable".
He said the justice secretary was "labouring under a very serious misunderstanding" of the way the EU works, and had a track record in the referendum debate of "coming out with statements which simply don't bear proper scrutiny".
'Period of uncertainty'
And Chancellor George Osborne told MPs that it was an "internationally accepted principle" that EU members cannot have access to the single market without accepting the free movement of people across the union.
However Mr Gove laughed off Conservative tensions when asked whether he was offended by Mr Osborne's description of the Leave campaign's arguments as "economically illiterate".
"No. George has called me much worse in private and in public," he replied.
Responding to Mr Gove's comments, MP Alan Johnson, chairman of Labour's In campaign, accused him of wanting to "wish away reality" but and leaving the EU "will hurt our economy".
"The fact is Britain is better off remaining in the EU and no amount of false promises and bluster from the Leave camp can change that," he added.
Analysis by the Treasury released on Monday warned that the UK economy could be 6% smaller by 2030 by leaving the EU rather than staying, and chancellor George Osborne said this would mean a £36bn hole in the public finances.
Giving evidence to the House of Lords Economic Affairs Committee, Bank of England Governor Mark Carney said he thought the report's "broad approach, to me, makes sense" but that it was not an "economic forecast" like those provided by the Office for Budget Responsibility.
He said a vote to Leave "might result in an extended period of uncertainty about the economic outlook" which would be likely to affect demand in the short term and could affect the supply side economy.
But the Leave camp - whose backers also include Mayor of London Boris Johnson and UKIP leader Nigel Farage - say the Treasury report's projections are based on assumptions that net migration to Britain, currently more than 300,000 a year, would remain well above the 100,000 target in the coming years - levels which, they say, are unsustainable.
Meanwhile, the president of the European Commission has said the EU is "interfering" in too many aspects of its residents' private lives.
Jean-Claude Juncker told a meeting of the Council of Europe that the European project had "lost part of its attractiveness" but the EU's executive arm was taking steps to address it.
"I think one of the reasons why European citizens are stepping away from the European project is due to the fact that we are interfering in too many domains of their private lives and in too many domains where member states of the European Union are better placed to take action and to pass through legislation."