Johnson, who is known in Britain and beyond for his often-outlandish persona and disheveled mop of platinum hair, made the remark while presenting an award to former finance minister George Osborne at the Spectator Parliamentarian of the Year Awards.
Brexit battle reaches UK's high court in challenge to PM
"Brexit means Brexit, and we're going to make a titanic, er titanic success of it," Boris, who campaigned for Brexit, said, according to a recording of the speech posted by the Spectator's editor.
After being informed that he had used the word "titanic", Boris told the audience that a Titanic exhibition in Northern Ireland was the most popular tourist attractions of the province. It was unclear why the exhibition was important.
Boris then clarified the remark by saying: "We are going to make a colossal, a colossal success of Brexit."
Prime Minister Theresa May's appointment of a man who in the run-up to the referendum compared the goals of the EU to those of Adolf Hitler and Napoleon caused consternation in European capitals.
Johnson originally made his name as an EU-bashing journalist in Brussels, then entered politics in the Conservative Party while also raising his profile through a series of appearances on a television comedy.
Johnson drew accusations of racism during the Brexit campaign by suggesting in a newspaper article that US President Barack Obama, whom he described as "part-Kenyan", was biased against Britain because of an "ancestral dislike of the British empire".
Britain 'will allow EU citizens to stay' after Brexit
He also drew the ire of Russia last month when he said he would like to see demonstrations outside its embassy in London. Russia said the comments were shameful, while French Foreign Minister Jean-Marc Ayrault questioned the wisdom of Johnson's remark about a demonstration.
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