During a speech in Manchester on Thursday, the minister said he plans for the UK to become an independent member of the World Trade Organisation (WTO).
Fox's comments represent a clear signal that he does not believe the UK should seek a "soft Brexit", involving membership of the EU single market or customs union.
He said Britain’s “brave and historic” decision to leave the EU will put the UK in a prime position to become a world leader in free trade.
The international trade secretary said, “The UK has a golden opportunity to forge a new role for ourselves in the world, one which puts the British people first.
Nick Clegg, former deputy prime minister and Lib Dem MP
Liam Fox is delusional about the impact of Brexit
“Those who believe that the referendum was a sign of Britain looking inwards have it completely wrong – it is the beginning of Britain increasing its global engagement.
“We are leaving the EU, we are not leaving Europe and we are ready to take our place in an open, liberal and competitive globalised trading environment.”
In his first major speech about trade after the EU vote, the minister urged European leaders to work with the UK in order to agree on new trade deals, arguing that otherwise future generations would be hit by the damaging economic consequences.
“Who does it harm more if we end up in a new tariff environment? It is in everyone’s interests that we have at least as free trading environment as we have today, anything else may not harm institutions but it will harm the people of Europe and it is the people of Europe who should be at the forefront of our thoughts.”
He also warned against countries opting to operate as “closed economies”.
Fox said, “In 1945, both North and South Korea began from a very similar base, but while South Korea embraced open trade and free markets, Pyongyang turned inwards with the tragic consequences for its citizens that we see to this day.
“There is a reason why those who wish to diminish political freedoms try to have closed economies because they know that, especially in the era of the technical revolution that is the Internet and social media, open markets will sweep in empowering and liberalising ideas.”
Nick Clegg, a Liberal Democrat MP, said on Twitter, “Liam Fox is delusional about the impact of Brexit. Leaving EU’s Customs Union and single market means deluge of Brexit red tape for UK businesses.”
Markus Kerber, chief executive of BDI, Germany’s biggest business lobby group, said he believes the British government hopes to secure full access to the single market and limited free movement of people.
“That, I think, is impossible at the moment. What we think the British government wants I can tell you straight away is not what the continental Europeans are willing or even able to give – then it will be relatively short negotiations,” he told the BBC.
Also on Thursday, a report from the Institute for Government revealed the government will need an extra 500 new staff to deal with the EU exit negotiations, costing up to £65m a year.
The government created two new departments to deal with the negotiations, the Department for Exiting the EU and the Department for International Trade.
David Davis, secretary of state for exiting the EU, has said that the department will need to take on at least an additional 320 staff, making a total of around 400.
Adding to the forecasted 200 extra staff needed for the trade department, the Institute for Government estimated that these additional staff will add up to £65 for every year that the departments operate.