"To present the nation with a choice between two deeply unattractive outcomes, vassalage and chaos, is a failure of British statecraft on a scale unseen since the Suez crisis", Johnson said.
"My brother Boris, who led the leave campaign, is as unhappy with the Government's proposals as I am", he said.
Quitting as junior transport minister, Johnson called May's Brexit plans "delusional" and said he could not vote for the deal she is expected to unveil in parliament within weeks.
Brexiteer Tory MP Andrea Jenkyns tweeted that she did not agree with him about another referendum - but his intervention highlighted unease on both sides of the debate, with the PM's efforts to secure a deal.
In an article sent to journalists, the MP for Orpington in Kent said the deal was being finalised in Brussels and Whitehall but the choice being presented was either, to back an agreement which would leave the United Kingdom "economically weakened with no say in the European Union rules it must follow" or a "no-deal Brexit" which would "inflict untold damage on our nation".
"Boris has resigned, now Jo Johnson, if they had any backbone they'd stay in their position and actually help the Prime Minister".
The only alternative on the table, he said, is a no-deal Brexit that would "inflict untold damage" on Britain.
Talks on Afghanistan, never said with Taliban, MEA spokesperson clarifies
The Afghan foreign ministry has emphasised that the council does not represent the Afghan government at the meeting, however. A Taliban delegation met with U.S. peace envoy Zalmay Khalilzad in Qatar in October to discuss ending the Afghan conflict.
Mr Johnson's resignation came just hours after Mrs May's de facto deputy said he hoped a deal would result in a "new dynamic" at Westminster, with MPs rallying behind the Prime Minister.
'It is now my intention to vote against this Withdrawal Agreement.
"I think then people will need to ask themselves what is it that is going to be in the best interests of those who sent them to Westminster to represent them, to ensure that we maintain living standards and investment and prosperity and employment in our country", Lidington added.
May's Downing Street office said on Twitter: "We will not under any circumstances have a second referendum".
Shadow Brexit minister Jenny Chapman said: "Jo Johnson is the 18th minister to resign from Theresa May's government".
"We may not have agreed about Brexit but we are united in dismay at the intellectually and politically indefensible". She has lost all authority and is incapable of negotiating a Brexit deal within her own party, let alone with the EU.
Calling for a second referendum, the Orpington MP said: "Given that the reality of Brexit has turned out to be so far from what was once promised, the democratic thing to do is to give the public the final say".
Boundless admiration as ever for my brother Jo.