Instead, EU nationals will need to confirm their right of residence in accordance with United Kingdom law.
The premier said she wants a reciprocal agreement to guarantee the rights of 1 million British citizens living in other European Union countries.
Setting out details of her proposal, May said Europeans who have been living in the United Kingdom for five years will get a new "settled status" after Brexit, giving them the same rights as British citizens to bring family members into the country.
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.
Those more recently arrived would be allowed to stay until they achieved this status.
More than three million Europeans are now living in Britain and around one million Britons living elsewhere in the EU. The European Parliament's chief Brexit negotiator, Guy Verhofstadt, said Monday that "a number of limitations remain worrisome and will have to be carefully assessed".
At home the UK Prime Minister agreed a pact with the 10 members of Parliament from Northern Ireland's Democratic Unionists, the DUP, to shore up her majority in what critics have called a two billion dollar cash-for-votes deal.
The EU has said before tackling trade and their future relationship that there needs to be "significant progress" on EU priorities, including its demand that Britain settle a "Brexit bill" and the rights of expatriate citizens.
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One thing which is certain is that all European Union citizens living in the United Kingdom after Brexit will need to apply for residence documentation confirming their right to live in the UK.
Jeremy Corbyn called the offer "too little, too late", arguing that the United Kingdom should have made a unilateral offer in the aftermath of the referendum. The government paper says, at the earliest, it will be March 29, 2017 - when Theresa May triggered Article 50, marking the start of the formal Brexit process.
So with Brexit negotiations now underway, I will outline the UK's offer to secure the rights of these people.
And we intend to introduce a voluntary scheme to enable eligible EU citizens to apply for their residence document before the United Kingdom leaves the European Union - reducing uncertainty and making Brexit as smooth and efficient as possible for EU residents in the UK.
Mr Hammond went on: "Wise words, with some applicability to the Brexit negotiations although I try to discourage talk of "cake" amongst my colleagues".
Britain has promised to streamline the application system for "settled status", after Europeans applying for permanent residency complained of an 85-page document requiring proof of employment and all travel out of the country for the past five years.
The percentage, however, rises dramatically among highly-skilled European Union workers, with 47% of them said to be mulling the prospect of leaving the United Kingdom within the next five years.
We hope that the deal the United Kingdom is offering will be reciprocated for Britons living in Slovakia, who have also made important contributions.