The former foreign secretary urged the Cabinet to "chuck it out" as he said the agreement is "about as bad as it could possibly be".
The angry tirade came after yesterday's announcement that a draft divorce deal had been agreed by UK and EU negotiators.
Mr Johnson said he expected the deal to be "pretty much" what had been agreed a few week ago "we are going to stay in the customs union on this deal, we are going to stay effectively in large parts of the single market and that means it's vassal state stuff".
Boris Johnson tells me he wants to see Cabinet resignations tonight over Brexit deal. Calls for them to get tough - now is the time.
— Kate McCann (@KateEMcCann) November 13, 2018
Mr Johnson said he would vote against the deal, warning that the proposals would made a "nonsense of Brexit".
He told the BBC: "For the first time in a thousand years, this place, this Parliament, will not have a say over the laws that govern this country. It is a quite incredible state of affairs."
Mr Johnson added: "For the first time since partition, Dublin - under these proposals - would have more say in some aspects of the government of Northern Ireland than London.
Which ministers are likely to quit?
Penny Mordaunt, International Development Secretary
Esther McVey, Work and Pensions Secretary
Dominic Raab, Brexit Secretary
Liam Fox, International Trade Secretary
Andrea Leadsom, leader of the Commons
"I don't see how you can support it from a democratic point of view, I don't see how unionists can support it, and I don't see how you can support it if you believe in the economic and political freedom of this country."
He claimed the deal was "making a nonsense of Brexit so I hope the Cabinet will do the right thing and I hope they chuck it out".
Asked by Sky News what Mrs May's Cabinet should do, he said: "I think they should have some guts and determination and man-up and woman-up and chuck it out."
And amid speculation about possible ministerial resignations, Mr Johnson said he would "like to see some action" from them.
Sky News correspondent Kate McCann tweeted: “Boris Johnson tells me he wants to see Cabinet resignations tonight over Brexit deal. Calls for them to get tough - now is the time.”
Mr Johnson told the broadcaster the deal was a "total catastrophe". "This is just about as bad as it could possibly be," he said.
Ministers have been briefed one by one on the contents of a draft divorce deal reached by officials from the UK and EU after months of protracted talks.
Further individual briefings are expected on Wednesday ahead of the special meeting of the full Cabinet at 2pm.
Before that Theresa May will face the House of Commons for a session of Prime Minister's Questions.
The deal follows intense negotiation in Brussels, with measures to prevent a hard border on the island of Ireland the main stumbling block.
Irish broadcaster RTE reported that the deal involved one overall "backstop" in the form of a UK-wide customs arrangement - as sought by Mrs May - but with deeper provisions for Northern Ireland on customs and regulations.
The Guardian reported that an independent arbitration committee will judge when a UK-wide customs backstop could be terminated.
There will also be a review in July 2019 six months before the end of the transition period, at which it will be determined how to proceed - a new trade deal, the backstop or an extension to the transition period.