In the article, he called for "a new partnership and a new deal with our friends in the EU based on trade and cooperation, but without this supranational apparatus that is so out of date and is imitated nowhere else".
The mayor, who has recently announced his decision to campaign for a Brexit, called on Britons to "screw up our courage and go for change".
Johnson is among a number of high-profile politicians who have openly expressed support for a Brexit, but a majority of British cabinet ministers, including Prime Minister David Cameron, prefer staying in the EU.
On Sunday, Cameron said a Brexit would be a "gamble of the century," warning of the risks of leaving Europe to the country's trade, jobs and security.
"There is no doubt in my mind that the only certainty of exit is uncertainty; that leaving Europe is fraught with risk," he wrote in a commentary for The Sunday Telegraph.
Meanwhile, Scottish First Minister Nicola Sturgeon made her latest intervention into the EU referendum debate on Monday by warning she would push for a second Scottish independence referendum in the event of a Brexit.
In a speech in London, Sturgeon said she wanted "an overwhelming victory across all parts of the UK for remaining in the European Union" in the EU referendum in June.
"The European Union is good for the prosperity and well-being of individuals, families and communities across our country," she said.
Britain will hold a referendum on whether to remain in the EU on June 23. Earlier this month, Cameron agreed on a package of changes to British membership in the bloc after two days of marathon talks with leaders of other member states at an EU summit.
The British government's official position is that Britain should stay in a reformed EU.