The offer was made by UK Prime Minister Theresa May during a summit of EU leaders in Brussels on Thursday.
Many EU citizens in the UK, and Britons living abroad, are worried about their status once Brexit happens. The UK's exit deadline is 30 March 2019.
Under the plan, a new UK settled status would grant EU migrants who had lived in the UK for five years rights to stay and access health, education and other benefits.
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The proposals, which come on the first anniversary of the EU referendum are dependent on EU states guaranteeing Britons the same rights.
English teacher Kristina Howells, a Calais-based Briton who was in Parliament this week to present a petition from UK expats, said, "It is great that finally May is taking into account a more humanitarian approach towards EU citizens in the UK."
However, she added, "How confident are we? The question is that even though there is an element of optimism, there is still this notion of being used as pawns in a rather complex situation.
"Until we have written assurances by the EU courts that British citizens have the right of freedom within the European Union, and that our status within our adoptive countries is safeguarded, it is then that we will be able to finally sleep easily at night."
Former UK Labour MP Roger Casale, who runs New Europeans, a citizens' rights campaign group, said, "Theresa May's proposals are a simple restatement of existing immigration rules. They revolve around the five year criterion for permanent residence, entirely failing to address the exigent circumstances created by Brexit. It is astonishing how easy it is to create a good impression simply by appearing to stop doing something which you shouldn't have been doing in the first place.
"Even more so when you are the Prime Minister of Britain and it is clear as a bell that you have no intention of keeping your promises. Theresa May's 'offer' to EU leaders at a dinner in Brussels about what she intends to do with the 3.5 million of their citizens who are building their lives in the UK falls into that category."