The prime minister will say that under the new system, people will be given the right to live in the UK based on skills instead of where they come from.
Ms May’s attempt to shift the debate onto immigration and away from technical issues around the Irish border marks an effort to fight back against Eurosceptic Tories trying to depose her.
Labour’s Jeremy Corbyn will also give a speech on Monday attacking the PM’s approach as “a botched, worst-of-all-worlds deal”.
On Sunday the prime minister sought to underline how it is future relations with the EU, and not the “withdrawal agreement” including the controversial Irish “backstop”, that will deliver the Brexit people voted for in 2016.
Building on that theme, she will say in a speech on Monday: “In the future, outside the EU, immigration will continue to make a positive contribution to our national life, but the difference will be this – once we have left the EU, we will be fully in control of who comes here.
“It will no longer be the case that EU nationals, regardless of the skills or experience they have to offer, can jump the queue ahead of engineers from Sydney or software developers from Delhi.
“Instead of a system based on where a person is from, we will have one that is built around the talents and skills a person has to offer.”
Downing Street believes immigration will be central in the fight to win support for the prime minister’s Brexit deal, ahead of a critical vote in parliament due in December.
It is widely accepted that the issue was at the very heart of many people’s reasons for backing the Leave campaign, but it has not yet featured in the debate about the merits of the actual Brexit deal struck by Ms May.
She will add during her speech at the CBI in London: “Not only will this deliver on the verdict of the referendum.
“It should lead to greater opportunity for young people in this country to access training and skilled employment.”
The prime minister will travel to Brussels this week to see European Commission president Jean-Claude Juncker, ahead of a summit to sign off both the withdrawal agreement and outline future framework on 27 November.
But Eurosceptics are continuing their push to oppose her plans, to rally support against them in the commons and to raise enough letters calling for her resignation to force a vote of no confidence in her.
It currently looks doubtful that Ms May’s plans have enough support from Conservative benches to be passed by the commons, but No 10 are now beginning a drive to turn Tory MPs who are as of yet unsure how they will vote.
In his speech to the CBI, Mr Corbyn will criticise the government for spending two years negotiating a deal that he argues will “leave the country in an indefinite halfway house without a real say over our future”.
He will say: “If the prime minister is unable to negotiate an agreement that can win a majority in parliament and work for the whole country, Labour’s alternative plan can and must take its place.”
The opposition leader said that his plan would prioritise a “new comprehensive and permanent customs union”, a guarantee for workers’ rights and protections for consumers and the environment, and a strong relationship with the single market.
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.