Johnson, who was a leader of the "leave" campaign during Britain's 2016 EU membership referendum, used a speech in London to argue for "an outward-facing, liberal and global Britain" after Brexit.
"We would be mad to go through this process of extrication from the EU and not to take advantage of the economic freedoms it will bring," he said.
It was the first in a series of speeches by senior ministers that the British government hopes will show unity and energy around Brexit after months of prevarication and mixed messages.
But Johnson's speech highlighted divisions within the Conservative government over what kind of relationship Britain wants with the EU after it leaves the bloc in March 2019.
The EU is Britain's biggest trading partner, and some ministers, including Treasury chief Philip Hammond, want to stay as close as possible to its borderless single market and tariff-free customs union. Others, including Johnson, want a definitive break so Britain can pursue a distinct economic policy and new trade deals around the world.
With just over a year until Britain leaves the EU, the two factions are still fighting for supremacy in the U.K. government.
Johnson said Britain should not agree to accept EU rules in return for access to its markets, saying it would be "absurd if we had to obey laws over which we had no say and no vote."
"It seems extraordinary that the U.K. should remain lashed to the minute prescriptions of a regional trade block comprising only 6 percent of humanity," Johnson said.
He said "it's only by taking back control of our regulatory framework and our tariff schedules" that Britain can strike new trade deals with the United States and other countries.
Johnson is among favorites to replace Prime Minister Theresa May as Conservative leader. But his prominent role in the anti-EU campaign - and an earlier role as a Brussels-based journalist writing sometimes fanciful stories about the bloc's bureaucracy - has made him unpopular with pro-EU politicians and voters.
In his speech, Johnson sought to reassure voters who wanted to remain in the EU that "Brexit can be grounds for much more hope than fear."
"Brexit need not be nationalist but can be internationalist; not an economic threat but a considerable opportunity," he said.
Opponents of Brexit were unimpressed. Labour Party Brexit spokesman Keir Starmer said Johnson's speech showed he wanted "a Brexit of deregulation, where rights and protections are casually cast aside and where the benefits of the single market and the customs union are ignored."
Business groups cautioned that any barriers to trade with the EU could be harmful.
"We do not make the U.K. more attractive to the rest of the world by putting barriers in the way of trade with our biggest market," said Antony Walker, chief executive of technology industry body techUK.
And European Commission President Jean-Claude Juncker said Johnson's claim that the EU aimed to build a European super-state was "total nonsense."
"We are not the United States of America," Juncker told reporters in Brussels. "We are the European Union which is a rich body because we have these 27, 28 nations."
Lorne Cook in Brussels contributed to this story.
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