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.
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.
Source and more information: http://www.bbc.com/news/uk-politics-40403431