The pro-Brexit Tory MP said both the Nazi leader and Napoleon had failed at unification and the EU was "an attempt to do this by different methods".
Labour MP Yvette Cooper, from the Remain campaign, accused the ex-London Mayor of playing "nasty, nasty games".
Meanwhile, UKIP leader Nigel Farage has backed Mr Johnson to be the next PM.
Mr Farage told the Mail on Sunday he was a "Boris fan" and said he was backing Mr Johnson to succeed David Cameron, if the prime minister resigned following the EU referendum.
The referendum takes place on 23 June, when voters in the UK will be asked whether they want the country to stay in or leave the European Union.
Speaking to the Sunday Telegraph, Mr Johnson said European history had seen repeated attempts to rediscover the "golden age of peace and prosperity under the Romans".
"Napoleon, Hitler, various people tried this out, and it ends tragically. The EU is an attempt to do this by different methods," he said.
"But fundamentally what is lacking is the eternal problem, which is that there is no underlying loyalty to the idea of Europe.
"There is no single authority that anybody respects or understands. That is causing this massive democratic void."
His comments - which come as campaigners from both sides of the debate took to the streets to try to win over voters - prompted a fierce rebuke from the Remain campaign.
Former Labour minister Ms Cooper accused Mr Johnson of having a "shameful lack of judgement" and a willingness to play "the most divisive, cynical politics".
She added: "He should not try to play political games with the darkest and most serious chapter of Europe's history. The EU has played a critical role keeping peace in Europe ever since."
The exchange comes as the campaign on both sides of the debate stepped up a gear on Saturday.
With less than six weeks to go until the vote, polls have put the Remain and Leave campaigns at roughly 50-50.
Mr Cameron warned that leaving the EU would have a "devastating impact" on infrastructure projects.
Campaigning in his Oxfordshire constituency, he said "vital projects across every region of the UK" would lose "crucial funding".
Mr Cameron said projects that had benefited from such funding included new trains for the East Coast Main Line, the M8 motorway extension between Edinburgh and Glasgow and the expansion of research and teaching facilities at Oxford University.
Meanwhile, Labour leader Jeremy Corbyn encouraged his supporters at a rally in London to vote Remain, saying it was "not the European Union that's the problem - it's the Conservative government".
Campaigning in Bristol, Mr Johnson said the UK should leave because the EU had changed "out of all recognition from what we signed up for".
He said the UK's "aborted" negotiations with the EU showed it was "going in completely the wrong direction".
"All our attempts at reform are hopeless unless we vote to leave," he added.
Grassroots Out, which is also calling for the UK to leave the EU, held a series of nationwide events on Saturday.
The official Britain Stronger In Europe campaign said it staged about 1,000 events across the UK.