EU nationals who arrive in the UK during the transition period after Brexit will be eligible for indefinite leave to remain, the government says.
Sources say it is a compromise offer to the EU which wants citizens to have exactly the same rights as they do now during the transition period.
It means free movement of people is effectively set to continue until the end of the two year or so transition.
But the UK says new arrivals should not expect all the same rights as now.
The EU wants the transition period - which is intended to smooth the way to the future post-Brexit relationship between the UK and the EU - to last until 31 December 2020. The UK says it should last around two years from March 2019.
Those arriving in the UK after 29 March 2019, the day Britain leaves the EU, will have to register with the authorities if they want to stay longer than three months.
They will then be allowed to stay for five years "working, studying or being self-sufficient" to qualify to apply for indefinite leave to remain, part of the process of becoming a UK citizen.
EU citizens who have been continually living in the EU for five years by 29 March 2019 will be able to apply to stay indefinitely by getting "settled status".
They will be able to bring spouses and other family members to the UK automatically under EU free movement rules.
Those who arrive after Brexit day will also be able to bring family members to the UK under free movement rules, during the transition period.
But - in the main change to the current arrangements - when the transition period has ended they will have to abide by the rules that currently apply to British citizens who want to be joined by family members from outside the EU, such as the minimum income requirement.
Since July 2012, UK citizens and settled residents applying to bring a non-EU partner to the country must be earning at least £18,600 per year before tax. The threshold is higher for those who are also sponsoring children.
Asked how the Home Office proposals differed from free movement - something Theresa May has always insisted will end in March next year - the prime minister's spokesman said: "We'll have a registration system and some of their rights will be different.
"When we leave EU the free movement directive doesn't apply but during the implementation period people will be free to come and live, work and study here. It's for Brussels to respond, this is us setting out our position."
The Home Office is encouraging EU member states to "mirror" these rules for UK citizens moving to EU member states during transition.
But in a major sticking point with the EU, the UK is insisting EU citizens arriving in the UK during transition must have their rights defined and interpreted solely in UK law and through the UK courts.
British judges will not be able to refer questions of interpretation to the European Court of Justice, the Home Office says.
'Exactly the same'
Irish citizens will not be subject to the agreement and therefore will not need to register, the Home Office says in fact sheet explaining the changes.
When the transition period has ended, the UK will put in place a new immigration system which the Home Office says will "strengthen control of our borders and address the public's concerns about the impacts of unrestricted immigration from the EU on jobs, wages and public services".
Labour MP Yvette Cooper, chairwoman of the Commons home affairs committee, said: "We have been pressing the Home Office for some time to clarify the arrangements for EU citizens arriving during the transition period so it is sensible that they have finally done so.
"But they should be a bit more straight with people. This new paper reiterates the prime minister's line that the expectations of EU citizens arriving in the UK after our exit will not be the same as those who moved here before our withdrawal, yet it then goes on to provide a long list of ways in which arrangements will be exactly the same.
"The clock is ticking and there isn't time to negotiate or implement an entirely new system of immigration or citizens' rights by March 2019 and they shouldn't suggest that things will change next year when they won't."