The Prime Minister is said to have promised allies she will not tolerate the foreign secretary if he seeks to undermine the peace deal.
The Times reports on her Boris threats following a marathon all day summit at her Chequers country retreat.
In a letter to Conservative MPs later, May made clear that ministers who complained about her plan would be sacked.
She said: “As we developed our policy on Brexit I have allowed cabinet colleagues to express their individual views.
"Agreement on this proposal marks the point where that is no longer the case and collective responsibility is now fully restored."
It followed fears Mr Johnson would lead half-a-dozen Eurosceptics to quit.
May appears to have faced down Brexiteer Cabinet ministers after securing agreement on plans which will keep the UK closely aligned to Brussels.
The proposals, which will now be assessed by the European Union, would result in the creation of a new UK-EU free trade area for goods, with a "common rulebook".
But under the Government's plans the UK would be free to diverge from EU rules over services, a major part of the British economy, with ministers acknowledging this will reduce the levels of access available to European markets.
Free movement would also end, although the proposals include a "mobility framework" to ensure UK and EU citizens can easily travel to each other's territories and apply to study or work.
Brussels will be reluctant to support any plan which would risk splitting the single market, and ministers appeared to acknowledge this by agreeing to step up preparations for a "no deal" Brexit.
But Mrs May said she hoped the proposals, which will be produced in a formal White Paper next week, would enable talks with the EU to move forward.
The Soft Brexit agreement in 6 bullet points
But Pro-Brexit groups were scathing of the PM's Brexit blueprint.
In a withering assessment Leave Means Leave boss John Longworth said the PM had "totally misled" 17.4million voters and branded her plans a "fake Brexit".
Business leaders, who have raised concerns about the impact of Brexit on jobs and the economy, also welcomed the Cabinet agreement.
But Mrs May's position could still be under threat from Tory Brexiteers despite the Cabinet agreement.
Backbencher Andrea Jenkyns said she was "awaiting the detail" of the plans before deciding whether or not to support calls for a leadership contest.
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