Theresa May is laying out the post-Brexit "settled status" that will be offered to EU nationals in the UK as ministers deny they will become second class citizens.
EU nationals applying for visas to come to the UK after withdrawal will be subject to the same criminality checks as other foreigners as part of the Brexit settlement.
Brexit Secretary David Davis said details of the plans would be set out in a 15-page document on Monday, after EU leaders reacted dismissively to outlines of the proposals last week.
Mr Davis has moved to try to reassure the 3.2 million EU nationals in the UK that they would "effectively" have the same rights as British citizens.
He insisted he did not expect any EU nationals to be deported unless they had committed a crime, or security issues were involved.
Mr Davis insisted the residency rights package for EU nationals would be fair.
He told the BBC: "They get the same residence rights, the same employment rights, the same health rights, the same welfare rights, the same pensions rights and so on, almost the equivalent to British citizens.
"The only thing they don't get is the right to vote."
He said the Government was seeking to continue the European Health Insurance Card (EHIC) initiative that ensures free medical care across the EU.
"We're looking to see if we can get a continuation of the EHIC scheme as it now exists. And if we can't get one then we will provide one unilaterally."
Mr Davis said the cut-off point for EU nationals being resident in the UK to be eligible for the rights package would fall somewhere between Article 50 being triggered in March this year and Britain's leaving date of March 2019.
He said there would be a "fight" in Brexit negotiations over any role for the European Court of Justice in overseeing the rights of residents.
"The argument now is going to be more about whether the European Court of Justice has a say, and that is where the fight comes in."
Mrs May's offer on residency rights was branded "a first step, but not sufficient" by the president of the European Commission Jean-Claude Juncker at an EU summit last week.