The former transport minister accused the Brexit campaign - which was led, in part, by his brother Boris - of offering the public "a false prospectus" that bears little resemblance to the reality of the deal that the prime minister is to present to parliament.
Instead, Johnson said it would be proper to give the British public a chance to vote again because of the way the Brexit negotiations have evolved.
"It's up to (lawmakers) to take a stand, I've done so, if others feel that it's right for them to do so then good on them".
Jo Johnson said the choice being offered was between a "travesty of Brexit" under the deal being thrashed out by the Prime Minister and the European Union, or the "untold damage" of a no-deal Brexit.
Johnson, brother of former foreign secretary Boris, said of his resignation as transport minister: "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".
The sterling which had traded as high as 1.3072 against the US Dollar slipped to 1.2969 at the NY close and to 0.8742 versus the euro having been as high as 0.8692, just two points above Thursday's six month sterling top of 0.8682.
Shadow Brexit minister Jenny Chapman said: "Jo Johnson is the 18th minister to resign from Theresa May's government".
Mr Johnson's sister Rachel said she was "hugely proud" of her "honourable and principled brother Jo who has put the interests of the country ahead of his political career".
He said it was an important message to all Conservative MPs who are "not saying what they think".
Gross domestic product (GDP) growth in the United Kingdom in Q3 stood at 0.6%, representing the fastest the economy has expanded since the fourth quarter of 2016, the ONS said.
Gross domestic product climbed 0.6pc in the third quarter, in line with analysts' expectations and up on growth of 0.4pc in the second quarter, the Office for National Statistics (ONS) said in an initial estimate.
She said: "Huge respect for Jo Johnson".