The ex-foreign secretary, who quit over Theresa May's Chequers Brexit plan, called her strategy "a moral and intellectual humiliation".
He said his vision would not lead to a hard Irish border, with any checks carried out away from the crossing.
The PM says her plan is the only one which will avoid carving up the UK.
And ex-attorney general Dominic Grieve, who backs a new referendum on Brexit, told the Evening Standard up to 40 Tory MPs were prepared to vote against any Canada-style deal if Mrs May ultimately opted for it.
BBC deputy political editor John Pienaar said Mr Johnson's 5,000 word article, published two days before the start of the Conservative Party conference, was a reminder that the PM's plan had very little support in the party and it was going to be a difficult week for her in Birmingham.
The UK is due to leave the EU on 29 March 2019. The two sides are seeking to negotiate the terms of exit, as well as an outline agreement on future co-operation. Parliament is to vote on any withdrawal deal.
In an article for the Telegraph titled "a better plan for Brexit", Mr Johnson wrote there had been a "collective failure of government, and a collapse of will by the British establishment, to deliver on the mandate of the people".
He said the Chequers proposals - which would keep the UK closely aligned with the EU in trade in goods - represented "the intellectual error of believing we can be half-in, half-out" of the EU.
UK firms would be exposed to EU regulations that could disadvantage them, and free trade deals would be made more difficult.
This, he said, was a "democratic disaster" and would "cheat the electorate" if implemented.
He proposed a looser free trade agreement, "at least as deep as the one the EU has recently concluded with Canada".
Canada's deal with the EU, signed in 2016, removes the vast majority of customs duties on EU exports to Canada and Canadian exports to the EU.
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