Johnson said of his resignation: "It has become increasingly clear to me that the Withdrawal Agreement, which is being finalised in Brussels and Whitehall even as I write, will be a terrible mistake."
He went on to call for a second Brexit referendum – a major policy difference between him and his Tory big beast brother Boris.
His resignation is a new blow to the PM who has been battling to reach on a consensus on Brexit within the Tories – seemingly failing to satisfy either sides of the divide.
Mrs May has been in Belgium and France today for Armistice Day memorial ceremonies with French president Emmanuel Macron and Belgian leader Charles Michel.
And it comes as the PM risks a row with coalition-partners the DUP, with a major rift opening up over the possiblity of a border down the Irish Sea.
“[This will be] a terrible mistake”
The proposed deal "will leave our country economically weakened, with no say in the EU rules it must follow and years of uncertainty for business" but the alternative is a no-deal Brexit which "will inflict untold damage on our nation", Johnson said.
Calling for a second referendum, he added: "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.
"This would not be about re-running the 2016 referendum, but about asking people whether they want to go ahead with Brexit now that we know the deal that is actually available to us, whether we should leave without any deal at all or whether people on balance would rather stick with the deal we already have inside the European Union."
QUIT: Jo Johnson warned Brexit in its current form will be a 'terrible mistake' (Pic: GETTY)
Johnson added: "Indeed, the choice being presented to the British people is no choice at all.
"The first option is the one the Government is proposing: an agreement that will leave our country economically weakened, with no say in the EU rules it must follow and years of uncertainty for business.
"The second option is a no-deal Brexit that I know as a transport minister will inflict untold damage on our nation.
"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."
BROTHERS: Boris Johnson heaped praise on Jo – but said he disagree with calls for another vote (Pic: GETTY)
PRIME MINISTER: Theresa May has been in France today with Emmanuel Macron (Pic: GETTY)
Boris wrote: "Boundless admiration as ever for my brother Jo.
"We may not have agreed about brexit but we are united in dismay at the intellectually and politically indefensible of the UK position.
"his is not taking back control. It is a surrender of control. It does not remotely correspond to the mandate of the people in June 2016."
Tory MP Conor Burns MP wrote: "Spot on Jo. This cannot go on."
BREXIT CRISIS: Theresa May is facing a fight over leaving the EU when she returns to Number 10 (Pic: AFP)
Meanwhile, DUP leader Arelene Foster has told RTE News that she will not support Theresa May's decision to have a Northern Ireland-specific backstop which will see a border down the Irish Sea: "No unionist would be able to support that," she said.
"In other words we (Northern Ireland) will have a different regulatory system from the rest of the United Kingdom, and essentially there's going to be a border down the Irish Sea."
The Prime Minister relies on the support of the DUP's 10 MPs for her Commons majority, votes which may become crucial as she attempts to get a deal through Parliament.
A Downing Street spokesman said: "The Prime Minister's letter sets out her commitment, which she has been absolutely clear about on any number of occasions, to never accepting any circumstances in which the UK is divided into two customs territories.
"The Government will not agree anything that brings about a hard border on the island of Ireland."
FLOOD GATES: What will Jo Johnson's stand against Brexit mean for the Cabinet? (Pic: GETTY)
Downing Street has played down suggestions that a Brexit deal is imminent, after European Council president Donald Tusk appeared to indicate a breakthrough could come within the next week.
A senior source said: "It does not feel to me like things are going to move today."
Cabinet ministers have been on stand-by for an emergency session to review any potential deal, but the source said that "nothing is going to happen" in terms of a meeting over the weekend.
A potential sticking point could be demands for EU fishing fleets to be given continued access to British coastal waters as the price for agreeing to Mrs May's UK-wide backstop.