Johnson said his constituents "deserve better" than a choice between May's "completely unacceptable" proposed deal and no deal.
"My view is that this is so different from what was billed that it would be an absolute travesty if we don't go back to the people and ask if they want to exit the European Union on this extraordinarily hopeless basis".
"We will be - instead of in Europe but not run by Europe, we will be out of Europe and yet wholly subject to European rules".
The deal being negotiated with Europe by the government - dubbed the "Chequers Deal" - would leave Britain economically weakened with no say in European Union rules it would have to adhere to for years, while a "no deal" scenario would inflict damage on the country.
At the same time, the sources claimed that Brussels isn't sure whether Prime Minister Theresa May's Cabinet approves of her plans.
"It has become increasingly clear to me that the withdrawal agreement, which is being finalised. even as I write, will be a bad mistake", he wrote in a stinging resignation statement.
The choice being presented to the British people was no choice at all, he said in an online article, announcing his resignation.
He added that the deals on offer could "inflict untold damage on our nation".
To give the public a choice between these two disastrous versions of Brexit would be a "failure of British statecraft on a scale unseen since the Suez crisis", he said, referencing the 1956 conflict against Egyptian President Gamal Abdel Nasser that is widely seen as marking the moment at which Britain formally lost its imperial role in the world.
Johnson's criticism underscored the travails that May faces in getting any Brexit divorce deal, which London and Brussels say is 95 percent done, approved by her own fractious party.
The British prime minister, in turn, reportedly reassured her colleague that she was still committed to a full backstop despite Raab's comments.
"I think that MPs, MEPs too. will be looking at what that deal says", the Cabinet Office minister said.
In an open letter today he wrote: " The government may have to take control of prioritising which lorries and which goods are allowed in and out of the country, an extraordinary and surely unworkable intervention for a government in an advanced capitalist economy.
"I hope and I believe that we can secure that majority in Parliament for the agreement".
"My brother Boris, who led the leave campaign, is as unhappy with the Government's proposals as I am".
It casts further doubt on Mrs May's chances of pushing her Brexit deal through the Commons.
The resignation is not just significant for the government's immediate plans, but also is yet another vote in parliament that could reject the Brexit plan, leaving the whole project in a crisis without any clear resolution.