And he urged Tory delegates to persuade the prime minister to "chuck Chequers" and return to the hard Brexit blueprint she first set out in her Lancaster House speech, when she said she would take the United Kingdom out of the customs union, single market and jurisdiction of the European Court of Justice.
The room erupted into cheers when he said Ms May needed "to chuck Chequers", as her Brexit proposals are known.
"They want to support a party that is decent, moderate and patriotic".
Johnson was a leading campaigner for Brexit in the referendum.
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"We will never do anything that would undermine the principles of our union - never!"
"This is the moment to chuck Chequers", he said.
"If we cheat the electorate, and Chequers is a cheat, we will escalate that sense of mistrust."
Johnson also set out a way to fight the Labour leader, who solidified the socialist takeover of the Labour party at the opposition's conference in Liverpool last week, pledging lower taxes and a free-market economy that gives people a stake in the country's future and control over their day-to-day life.
He added: "I don't think this is a time to be talking about leadership challenges, it is a time to be supporting our Prime Minister as she takes forward this incredibly hard task of getting a deal with the European Union".
Satirist Kaya Marr holds a painting mocking MP Boris Johnson outside the conference in Birmingham on Tuesday.
"I passionately believe that our best days lie ahead of us and that our future is full of promise", she will say, stressing: "Don't let anyone tell you we don't have what it takes: we have everything we need to succeed".
Other ministers chimed in, with Justice Minister David Gauke doubting Johnson's credentials for leadership.
In his letter to Brady, Duddridge said that he is normally a loyalist, and has never voted against the government until now.
Ian Livermore, 65, from south Gloucestershire said the speech was "superb" and showed why Johnson should be leader.
He said: "Building a bridge between mainland Britain and Ireland, the latest intervention of Boris Johnson, who normally burns bridges instead of building them".
"Am I disappointed [that he didn't declare]?"
"We have a very, very strong leader in Scotland in Ruth Davidson who had a very significant contribution to make to this conference".
Her speech comes after Boris Johnson launched a fresh broadside against her Chequers plan for trade with the EU.
And he added: "The Prime Minister seems incapable of doing this".
Mr Johnson warned that voters would not forgive the party for "bottling Brexit".
Mr Johnson said that Mrs May's blueprint - which ties Britain to a common rulebook with the European Union for trade in goods - would be "politically humiliating for a £2 trillion economy" and would prevent the United Kingdom from making its own laws and subject it to the directives of Brussels.
Ranting before MEPs on Tuesday, arch-liberal and federalist Guy Verhofstadt also personally attacked senior members of the Tory Party and rejected proposals from leadership favourite Boris Johnson to extend the Article 50 process.
"Chequers has failed, it's not realistic, it doesn't deliver on the Brexit my constituents vote for".