Mr Rees-Mogg insisted the PM's deal represented a "complete Brexit" - and called on Mr Farage to recognise the campaign to leave the European Union had been a success.
"An incoming Labour government will first secure a sensible deal".
He said the Tories had delivered despite critics arguing "it couldn't be done" as he urged his allies to help him defeat Mr Corbyn on December 12 and cautioned a Labour government would be "calamitous" for the UK.
The Brexit Party chief said Johnson's ruling Conservatives could pay dearly for rejecting his offer for a "non-aggression pact" in the December 12 snap election.
Jo Swinson, the Lib Dem leader, launched her party's campaign as she set out plans for a £50 billion "Remain bonus" which could be spent on improving the United Kingdom if it stays in the EU.
He added Mr Johnson was "trying to cash in the votes of millions who voted to leave the European Union, to buy political power for himself and then sell them out". Many people who voted to leave tell me they were voting for change. Senior NHS managers have said that would mean "higher prices for medicines" which will "pass on costs to both patients and the NHS".
Johnson's Conservatives deny planning to lower standards, and say they are confident of finishing the negotiations by the end of 2020, when a transition period laid out in the proposed divorce agreement is due to end.
That latter outcome could mean The Brexit Party becomes kingmaker after the December vote - playing a role similar to that currently held by the now marginalised, angry and activist Democratic Unionist Party of Northern Ireland - which would nearly certainly mean the prospect of a "no deal" Brexit is kept alive and well over the coming years. So we'll say it again and again until the message gets through to the White House: "our NHS is not for sale".
In a chant taken up by many in the room Mr Corbyn said: "Our NHS is NOT FOR SALE". From the USA, trade balance, ISM non-manufacturing PMI and number of jobs available will be released. It's not happening by accident.
Mr Corbyn added that the Conservatives were preparing to "unleash Thatcherism on steroids", offering up the health service to U.S. pharmaceutical firms and diminish workers' rights, food standards and efforts to reduce pollution.
Mr Johnson told his Cabinet members they are heading towards an election "none of us particularly wanted to hold". What Boris Johnson's Conservatives want is to hijack Brexit to unleash Thatcherism on steroids.
"The difference between Boris Johnson and Jeremy Corbyn is the difference between a Premiership goal scorer and someone who is, I'm afraid, a non-league player".
He wrote: "When they choose the next Prime Minister, the voters deserve to have a clear picture of what each potential leader will do when it comes to Brexit".