"After the United Kingdom has left the European Union, EU citizens with settled status will be able to bring family members from overseas on the same terms as British nationals", she said.
The EU citizens who have held five years of continual residence in the U.K.at a cut off point, which is still to be determined, will be treated as they are United Kingdom citizens in terms of healthcare, education, benefits and pensions, according to government plans set out in a document published Monday.
May received a cool reception when she set out the principles of her plan to European leaders at a summit on Thursday, with EU President Donald Tusk warning that it fell "below our expectations".
Jeremy Corbyn, leader of Britain's main opposition Labour Party, said May's reduced stature after losing her parliamentary majority in an election on June 8, meant that she could no longer wring out a good deal for Britain from the EU.
Any European citizen remaining in the United Kingdom after the date Britain leaves the EU will be forced to apply for a new "residence document" in order to achieve "settled status" allowing them to stay in the UK.
"After the United Kingdom has left the European Union, EU citizens with settled status will be able to bring family members from overseas on the same terms as British nationals".
Theresa May has also said people who apply for settled status will have to undergo criminal record checks and will be rejected if they are "serious or persistent criminals and those whom we consider a threat to the UK".
The cut-off date will be the subject of discussions, but will be no earlier than 29 March 2017 - when Article 50 of the Lisbon Treaty was invoked - and no later than March 29, 2019, the date the United Kingdom leaves the EU.
Those Europeans arriving after the cut-off date will be given a "grace period", likely two years, to apply for another form of immigration status allowing them to legally reside in Britain, such as a work permit.
The government's 17-page policy plan would allow Europeans to stay in post-Brexit Britain with broadly the same rights as Britons, with access to healthcare, education, welfare and pensions.
"I want to completely reassure people that under these plans, no European Union citizen now in the United Kingdom lawfully will be asked to leave at the point the United Kingdom leaves the EU".
British citizens now seeking to bring a non-EU spouse to the United Kingdom face similar barriers.
- Qualifying EU citizens will have to apply for residence status.
"The UK's withdrawal from the European Union raises hard questions about the future trading relationship between the two jurisdictions", the Zurich-based Global Reinsurance Forum, which represents some of the world's largest reinsurers, said in the letter sent in April.
However it is thought that the United Kingdom is reserving the option of setting an early cut-off for residency rights in case there is a late surge of migrants arriving as Brexit approaches.
Verhofstadt warned that "any degradation of the rights linked to freedom of movement" before Britain leaves the European Union would be contrary to European Union law.