Theresa May has said she wants EU citizens living in the UK to stay after Brexit as she announced plans designed to put their "anxiety to rest".
All EU nationals lawfully resident for at least five years will be able to apply for "settled status" and be able to bring over spouses and children.
Those who come after an as-yet-unagreed date will have two years to "regularise their status" but with no guarantees.
Jeremy Corbyn said the offer was "not generous" and "too little, too late".
Labour said the UK should have made a unilateral guarantee of security to EU citizens in the aftermath of last year's Brexit vote.
The EU's chief negotiator said the proposals did not go far enough.
A 15-page document outlining the detail of the UK's offer to EU citizens was published as Theresa May briefed MPs on the outcome of Friday's EU summit - at which she first set out her plans.
She told the Commons that she wanted to give reassurance and certainty to the 3.2 million EU citizens in the UK - as well as citizens of the three EEA countries and Switzerland - who she said were an "integral part of the economic and cultural fabric" of the UK.
But she said any deal on their future legal status and rights must be reciprocal and also give certainty to the 1.2 million British expats living on the continent after the UK leaves the EU - expected to be on 29 March 2019.
The key points of the UK's proposals are:
- Those granted settled status will be able to live, work, study and claim benefits just as they can now
- The cut-off date for eligibility is undecided but will be between 29 March 2017 and 29 March 2019
- Family members of EU citizens living abroad will be able to return and apply for settled status
- EU nationals in the UK for less than five years at the specified date will be able to continue living and working in the UK
- Once resident for five years, they can apply for settled status
- Those arriving after the cut-off point will be able to stay temporarily
- But there should be "no expectation" they will be granted permanent residence
- A period of "blanket residence permission" may apply to give officials time to process applications to stay in the UK
- The Home Office will no longer require evidence that EU citizens who weren't working held "comprehensive sickness insurance"
The prime minister told MPs that those granted settled status, equivalent to having indefinite leave to remain, would be "treated as if they were UK citizens for healthcare, benefits and pensions".
Mrs May said the process of application would be simplified and a "light touch" approach adopted. The existing application process for permanent residency, which involves filling out a 85-page form, has been widely criticised.
"Under these plans, no EU citizen currently in the UK lawfully will be asked to leave at the point the UK leaves the EU," Mrs May said.
By Danny Shaw, BBC home affairs correspondent
Officials anticipate that the process of administering "settled status" will be a huge challenge, with some 3.2 million potential applications.
Those EU nationals who've been assigned residency cards already will have to apply again under the new system, though the process for them is expected to be "streamlined".
It's thought applications for settled status will start to be processed from mid-2018.
Officials say they intend to put in place a new, online, simplified system - but say they are used to dealing with large volumes of applications - 2.5 million visas each year and seven million passports.
Mrs May said spouses, children and other family members currently living overseas would be able to come to the UK and apply for settled status on the same basis as their partners and relatives.
Pressed by several Labour MPs, she suggested there would be no income barriers for anyone whose relatives have been in the UK for more than five years while, for others, existing rules applying to the foreign dependents of British citizens would be in force in future.
"There will be no extra requirements," she said. "We are not talking about splitting up families."
She also insisted the UK should police the new rules rather than the European Court of Justice.
But Mr Corbyn said the question of citizens' rights should have been dealt with in isolation rather than being dragged into the "delicate and complex" matrix of trade and other Brexit-related issues now being discussed.
"The truth is it is too little, too late. That could have been done and should have been done a year ago when Labour put that very proposal to the House of Commons. This isn't a generous offer. This is confirmation the government is prepared to use people as bargaining chips."
The SNP's Ian Blackford said there were still "more questions than answers" about how EU citizens living in Scotland would be affected.
EU chiefs react
And the Joint Council for the Welfare of Immigrants said it could not understand why those who already had permanent residence were being asked to re-apply to obtain the new status.
"These are people who have already proven their right to be here to the government's satisfaction under a very stringent process," said its chief executive Saira Grant.
"It is astonishing that the government wants to take on the expense and administrative hassle of reprocessing all of those applications under a new scheme."
Reacting on Twitter, Michel Barnier, who is leading the Brexit negotiations for the EU, said his goal was the same level of protection that citizens currently have under EU law.
He added: "More ambition, clarity and guarantees needed than in today's UK position."
Another key EU figure, Guy Verhofstadt, who is negotiating on behalf of the European Parliament, warned that any changes to free movement laws before the UK has left would break EU law.