The plan, which will 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".
A new "facilitated customs arrangement" would remove the need for checks and controls by treating the UK and EU as if they were a "combined customs territory".
The Prime Minister managed to secure agreement with her Cabinet, including Brexiteer members, after a marathon session of talks at Chequers on Friday.
But as details of the agreement emerged, Tory Eurosceptics warned Mrs May they might not accept a plan which saw her "red lines" turn pink.
The common rulebook for goods, including food and agricultural products, could limit the UK's ability to strike trade deals with countries such as the US, for whom securing market access for American farmers would be a big prize.
Jacob Rees-Mogg, leader of the influential European Research Group of pro-Brexit Conservative MPs, said he wanted to see more details of what had been agreed.
He warned that the common rulebook proposal could make "trade deals almost impossible" if it meant regulations would have to apply to any goods coming into the UK.
He added that "it is possible that this deal is worse" than a "no deal" Brexit.
"As with eggs: an egg that is very softly boiled isn't boiled at all. A very soft Brexit means that we haven't left, we are simply a rule-taker," he told BBC Radio 4's Today programme.
"That is not something that this country voted for, it is not what the Prime Minister promised."
Backbencher Andrea Jenkyns said she was "awaiting the detail" of the plans before deciding whether to support calls for a leadership contest.
She said the common rulebook would mean "British businesses will continue to be a rule-taker from the EU".
Veteran Eurosceptic Sir Bill Cash told BBC's Newsnight he was "deeply disappointed, to say the least" and the plans "raise a lot of very serious questions".
The Prime Minister has told her Cabinet that collective responsibility rules are now being fully applied, meaning she will not tolerate criticism of what has been agreed.
Cabinet Brexiteers defended the plans in public, with Transport Secretary Chris Grayling saying: "I didn't campaign to leave the European Union to have a different specification of motor car on sale in the UK to the one that's on sale in France.
"This is simply saying that we will effectively sell the same products across Europe as we do now - it's what business does and would do anyway, nobody produces a different product for one country."
Asked what the common rulebook with the EU on food products would mean for the proposed US trade deal, Mr Grayling told Today: "There may be individual issues to address in future trade talks."
He stressed that the European Court of Justice's "remit in the UK will end when we leave" but "of course there will be a degree of looking from one group of judges to another".
Commons Leader Andrea Leadsom said: "As a passionate Brexiteer with huge optimism about future as a free trading nation, I agree with the PM that keeping the UK together is vital."
Business Secretary Greg Clark, one of the Cabinet ministers favouring close alignment to limit economic damage, welcomed the "very positive" outcome.
Pro-EU Tory Anna Soubry said she would "always welcome" a policy that delivers a "business friendly Brexit", adding that she had "no doubt" the Prime Minister would now enforce Cabinet discipline.
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 European Union's chief Brexit negotiator Michel Barnier said he was looking forward to the publication of the white paper and the EU would consider whether the proposals are "workable and realistic".
Business leaders, who have raised concerns about the impact of Brexit on jobs and the economy, also welcomed the Cabinet agreement.
CBI director-general Carolyn Fairbairn said it was a "genuine confidence boost" but added: "The hard work starts now, and time is a challenge."
Shadow Brexit secretary Sir Keir Starmer said: "It is farcical that it has taken two years for the Cabinet to even attempt to agree a position on the basics of our future relationship with the EU.
"On previous form, whatever has apparently been agreed will struggle to survive contact with Tory MPs and members."