But he said a second referendum is "not the way forward and is not supported by the public".
"But 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 bad mistake".
Still under the No Deal scenario "Britain stands on the brink of the greatest crisis since the Second World War", he said.
Scottish politicians opposed to Britain leaving the European Union had successfully asked for a ruling to clarify whether Britain could withdraw its notification to leave without permission from the bloc's other members.
The ex-transport minister said: "Hopes for the easiest deal in history have proved to be delusions".
Boris Johnson, who himself resigned over May's Brexit plans, backed his brother's decision, saying: "We may not have agreed about Brexit but we are united in dismay at the intellectually and politically indefensible of the UK position".
Transport minister, Jo Johnson, has resigned over Theresa May's Brexit plan.
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The only alternative on the table, he said, is a no-deal Brexit that would "inflict untold damage" on Britain.
The MP, who is Boris Johnson's brother, said the withdrawal deal now being negotiated with the European Union "will be a awful mistake".
"If these negotiations have achieved little else, they have at least united us in fraternal dismay".
"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".
Jo Johnson's resignation, and his call for a fresh referendum to test voter sentiment, further complicates matters for May as she tries to strike a deal with European Union leaders that would pass muster with her own cabinet and win backing in Parliament.
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. 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.
His older brother Boris wrote on Twitter after the announcement: 'Boundless admiration as ever for my brother Jo.
"We are barreling towards an incoherent Brexit that is going to leave us trapped in a subordinate relationship to the EU", he said.