In a blog for Medium, Johnson, brother of arch-Brexiteer and former foreign secretary Boris Johnson, writes: "Although I voted Remain, I have desperately wanted the government, in which I have been proud to serve, to make a success of Brexit: to reunite our country, our party and, yes, my family too".
In his resignation statement, Johnson said the mooted deal would leave Britain "economically weakened, with no say in the European Union rules it must follow and years of uncertainty for business".
Mr Johnson, younger brother of Boris, used his resignation to call for a second vote, claiming it was now "imperative" to go back to the public to "check they are content" with Mrs May's proposals for Brexit.
This is despite the fact he reportedly wrote the 2015 election manifesto for the Tory party promising to "honour the result of the  referendum, whatever the outcome".
His brother Boris - who also quit Mrs May's Cabinet over Brexit - immediately backed Jo over the government's "intellectually and politically indefensible" position of the government.
'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, ' said Jo Johnson in an online article sent to journalists.
Jo Johnson's decision to quit as transport minister saw pro-EU and arch-Brexiteers in the Conservative Party unite to attack the Prime Minister's stance.
"There are difficulties in getting this withdrawal agreement, we understand what those are and we're working our way through them".
The DUP leader said "no unionist" could back Mrs May's apparent advocacy of a withdrawal treaty that includes a Northern Ireland specific backstop measure to avoid a hard border on the island of Ireland.
Mr Johnson, whose bombshell resignation as transport minister took Westminster by surprise, said if other senior Tories followed suit, "good on them".
"I've done so, if others feel that it's right for them to do so, good on them".
Downing Street spokesman said the referendum "was the biggest democratic exercise in this country's history".
"The Prime Minister thanks Jo Johnson for his work in Government".
He called for a new public vote on leaving the EU. "If these negotiations have achieved little else, they have at least united us in fraternal dismay", he said.
Prime Minister Theresa May this week faced pressure from her Westminster allies in the Democratic Unionist Party not to allow a customs border to split Northern Ireland from the United Kingdom after Brexit.