But the EU's top negotiator Michel Barnier said Britain needed "more ambition, clarity and guarantees" in its position.
Introduction of a new system - 'Settled status:' For EU nationals who have lived in the United Kingdom for five years on a continuous basis, there is the opportunity to gain "settled status", which would allow them to enjoy the same rights as British citizens.
The right to apply for the new status will apply to family members and partners resident in the United Kingdom at the cutoff date, including those "who do not yet have five years' residence".
It's also a measure of the challenge facing the UK Prime Minister: Fighting to hold her government together on one front and for Brexit in Brussels on the other.
However it was condemned as "too little, too late" by Jeremy Corbyn who said the Government should have seized the initiative by unilaterally guaranteeing the rights of European Union nationals after last year's referendum vote to leave the EU.
The Government wants people to start applying before the Brexit arrangements are finalised.
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Those EU citizens who arrived and became resident for a shorter period at the time of the UK's exit will be able to apply for temporary status in order to remain resident in the United Kingdom until they have accumulated five years, after which they will be eligible to apply for settled status.
In her statement, the Prime Minister said European Union nationals granted settled status would be treated "as if they were United Kingdom citizens for healthcare, benefits and pensions".
Those who have been resident for less than five years will also be allowed to stay and then apply for settled status after five years.
Formal negotiations on Brexit started last week, with Britain's European Union departure expected in March 2019.
Britain could face a serious shortage of skilled workers after Brexit, with nearly half of European Union citizens working in the United Kingdom said to be ready to leave the country over the next two years.
European rules already allow member states to expel other EU citizens on security grounds, and between 4,000 and 5,000 EU prisoners were deported from Britain previous year, according to the interior ministry.
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May promised to end the "anxiety" of 3.2 million European nationals but is on a collision course with Brussels after vowing that the European Court of Justice would not be allowed to protect their rights.
However, May added that her "fair and serious" offer was conditional and based on the United Kingdom receiving a reciprocal deal from Brussels guaranteeing the rights of some one million British citizens living in the EU.
Guy Verhofstadt, the European Parliament's Brexit negotiator, said "a number of limitations remain worrisome and will have to be carefully assessed".
BBPA chief executive Brigid Simmonds added: 'I welcome that the Government has now set out proposals that make clear that staff in our industry can remain in the United Kingdom after Brexit.
The cut-off date will be the subject of discussions, but will be no earlier than March 29, 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. The government say exceptions may be made if they "have strong ties here" however the details of this have not yet been spelled out.
EU citizens will lose protection of the European Court of Justice.
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The UK paper also makes clear that Irish citizens, now covered by Common Travel Area agreement which they hope to sustain, will be unaffected.