The remain-backing MP for Orpington and rail minister published an article online saying he could not vote for the deal which May is expected to bring back to parliament within weeks and instead would be throw his weight behind a second referendum.
Still under the No Deal scenario "Britain stands on the brink of the greatest crisis since the Second World War", he said.
"The Prime Minister thanks Jo Johnson for his work in government".
Britain could be about to finally seal an all-important deal to smooth its departure from the European Union, although reports this week of an imminent announcement have cooled somewhat heading into the weekend.
She has lost all authority and is incapable of negotiating a Brexit deal within her own party, let alone with the EU.
Calling Theresa May's Brexit deal "a bad mistake", the minister of state for transport quit his post, claiming the United Kingdom economy would suffer from May's Brexit agreement.
Compounding May's problems on Friday, the Northern Irish party that props up her minority government cast her Brexit negotiation as a betrayal and said it could not support any deal that divided the United Kingdom.More news: California Fire Spreads To Kimye’s House & ‘Is So Close’ To Kylie’s!
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"This is the time for all of them, as Jo Johnson has done, to look deep inside their consciences, to reflect deeply on their responsibilities, and do the right thing for future generations".
Asked whether he believed the British public had changed its view on Brexit, he replied: "I think there's a great deal to suggest that the public are changing their view and that a lot of people now realise that in fact leaving the European Union in the way that it is projected, it's likely to leave us at a disadvantage".
Even a no-deal Brexit "may well be better than the never-ending purgatory" that Mrs May's plan would offer, he said. While Johnson's resignation is likely to spur critics in the Conservative Party, securing a second referendum would also require support from the Labour Party, which is yet to fully clarify its stance on a referendum and what that could entail in terms of the question put to the public.
He wrote: "Boundless admiration as ever for my brother Jo".
Johnson - who had backed staying in the bloc in the 2016 referendum - is the younger brother of Boris Johnson, who spearheaded the pro-Brexit campaign and quit as foreign secretary in July over May's Brexit blueprint.
Britain's government cannot stop a case seeking to determine whether the country can unilaterally reverse Brexit - due to be considered by Europe's top court on November 27 - Scotland's Court of Session ruled on Thursday.