A Downing Street spokesperson said: “The Cabinet agreed that, once free movement is brought to an end, the Government will be able to introduce a new system which works in the best interests of the UK – including helping boost productivity.”
The plans – which would kick in after the UK’s “implementation period” with the EU ends in December 2020 – were approved despite objections from some Cabinet ministers.
Philip Hammond and Business Secretary Greg Clark are said to have raised concerns that the new system could cause disruption to businesses if it is introduced suddenly.
A Whitehall source told the Times: “Philip Hammond did not argue to continue free movement, nor did he argue against curbs to low-skilled migration.
“What Greg Clark pushed for yesterday — and Philip Hammond agreed with him — was to avoid a cliff-edge policy which involves a sudden big change for business. They lost that argument.”
That reportedly prompted a dig at Mr Hammond from Work and Pensions Secretary Esther McVey.
According to The Guardian, she told him: “On the one hand, we’re told that when we leave the EU we will go into a recession.
“On the other, we’re going to need mass migration. They can’t both be correct.”
Mr Javid meanwhile made clear that the proposals will include some leeway for low-skilled migration to avoid shortages in industries heavily dependent on migrant labour.
The Home Secretary also confirmed that regions that strike a free trade deal with the UK – including the EU itself – could be given preferential access to the UK labour market under the plans.
The proposals are set to be fleshed out in a new immigration white paper in the autumn – and could feature in Theresa May’s speech to the Conservative party conference next week.
Cabinet ministers meanwhile stepped back from urging the Prime Minister to ditch her Chequers Brexit plan in favour of a Canada-style free trade deal.
Mrs May’s proposals – which aim to agree a “common rulebook” with the EU on goods – were ridiculed by her European counterparts at a meeting in Salzburg last week.
But she told the Cabinet to “hold our nerve”, at a “critical point” in the talks.
Brexiteers in the Cabinet were reported to be swinging behind a Canada-style deal currently being talked up Tory Eurosceptics.
But senior ministers have now given the Prime Minister extra time to try and sell her plan to the EU.
A Cabinet minister told The Sun: “There was a feeling that the PM did well on Friday with her No10 statement on Brexit, and she has earned some breathing space.
“But we are still left with the fact that the EU has said no to Chequers, and that is a problem that is not going to go away. So we will have to move on from Chequers if there is no movement from Barnier in two weeks.”
Brexit Secretary Dominic Raab meanwhile told reporters the Cabinet had had “a good, healthy discussion”.
He added: “The Prime Minister made clear we are going to keep our calm and press the EU on some of the criticisms they have made. But also to be clear that there are no credible alternatives the EU has come up with.”