The UK Prime Minister says she wants all EU citizens lawfully living in Britain to remain after Brexit in 2019.
Theresa May is also promising a streamlined system for them to register to be able to stay.
"They have made a huge contribution to our country, that's why we want them and their families to stay. I am absolutely clear that EU citizens living lawfully in the UK today will be able to stay," May said in parliament.
"It is going to be a digital system, it will be streamlined, it will be user-friendly and it will ensure that this is as simple and as easy a process for people as we can provide."
Why has May said this now?
Because negotiations are at a key stage between London and Brussels.
The EU wants May to clarify how she sees Britain's future relationship with the bloc.
It is pressing for a status-quo transition period. Brexit campaigners fear this will see the UK subject to new EU laws that could threaten the status of London's financial centre.
Why is David Davis on a tour of Europe?
He is visiting European capitals as Britain tries to persuade EU leaders to strike a new deal on trade. Britain wants to retain close economic ties with the EU after it leaves the trading bloc in March next yer, while also being free to strike new trade deals around the world.
Brexit minister David Davis said the UK and the EU could reach a deal to access each other's markets. He also dismissed fears Britain would use Brexit as an excuse to cut regulation to attract global businesses, despite past threats to do so.
Davis told business leaders in Austria that fears of the UK plunging into a "Mad Max-style world" borrowed from dystopian fiction after leaving the EU are unfounded.
Instead, he proposed a system of "mutual recognition" where both sides agree common regulatory outcomes like consumer protection or financial stability, while being able to pursue their own policies to reach those goals.
Citing workers' rights and financial regulation as areas that could be improved, Davis said the UK wants to work with the EU to create the highest standards of rules in the world.
His comments were designed to allay European politicians' concerns that Britain could cut taxes and regulation to attract global businesses.
His speech comes as the EU formulates its approach to the next stage of the Brexit negotiations and ahead of a crucial meeting on Thursday to decide on Britain's negotiating strategy.
What David Davis said
"This will be a crucial part of ensuring our future economic partnership is as open, and trade remains as frictionless, as possible."
"Britain's plan, its blueprint for life outside of Europe, is a race to the top in global standards, not a regression from the high standards we have now."
Davis said the UK and the EU could preserve regulatory standards by close cooperation between regulators and the use of an independent arbitration mechanism.
"The agreement we strike will not be about how to build convergence but what to do when one of us wants to make changes to rules."
"Such mutual recognition will naturally require close, even-handed cooperation between these authorities and a common set of principles to guide them."
He said the EU already has a number of mutual recognition agreements with countries such as Switzerland, Canada and South Korea covering products including toys, cars, electronics and medical devices.
What has the EU said?
EU leaders have warned Britain it can't have both freedom from the bloc's regulations and frictionless trade.
What is business saying?
Anxious to preserve cross-bordre supply chains, business leaders generally support the plan.
The speech provides "assurances that the government wants to maintain and improve standards that deliver for customers, whilst not inflicting any additional administrative burden on business," said Helen Dickinson, chief executive of the British Retail Consortium.
Since Britain voted to leave the EU in 2016, supporters of Brexit have argued that removing the costs imposed by EU rules would be one of the main benefits.