British Prime Minister Theresa May has said that her government and the EU are within "touching distance" of reaching an agreement on citizens’ rights.
The issue is one of three areas to be dealt with in current round of Brexit negotiations.
The other areas are the Irish border and the financial settlement which the UK must pay as it leaves the EU bloc.
In an open letter posted on her Facebook page and mailed to 100,000 EU nationals living in Britain ahead of tomorrow’s European Council meeting in Brussels, Mrs May promised to make it as easy as possible for EU citizens to obtain "settled status" in the UK.
And she has promised that the process for EU nationals to register to stay in the UK will be "streamlined" - with EU citizens having a direct say over how it will work.
EU citizens will be invited to sit on a new "User Group" that will "meet regularly", ensuring "the process is transparent and responds properly to users' needs".
There has been considerable concern among many European citizens living in the UK about what their status will be in post Brexit Britain.
Last week, Mrs May refused to say in an interview what it would mean for those people if no deal was reached between the EU and UK.
There has also been concern about how any rights would be overseen. Many EU citizens want that to fall to the European Court of Justice, a body which many Brexiteers do not want involved in any aspect of UK law after Brexit.
In the Facebook post, Mrs May said she knows EU citizens who have made their lives in the UK have made a huge contribution to the country, and she wants them and their families to stay.
Mrs May says she could not be clearer; EU citizens living lawfully in the UK will be able to stay in Britain.
Meanwhile, UK Labour Party leader Jeremy Corbyn will also travel to the Belgian capital to accuse Mrs May of "bungling" the withdrawal process and declare that Labour "stands ready to take up responsibility for the Brexit negotiations".
Mr Corbyn will meet three EU prime ministers, as well as chief Brexit negotiator Michel Barnier and European Parliament president Antonio Tajani.
Mrs May received a boost today, as European Council president Donald Tusk declared he will recommend that the EU27 begin "internal preparations for talks on the transition and the future relationship" which could begin as early as the next scheduled summit in December.
But Mr Tusk warned that progress in December would require "more concrete proposals from the British side", in comments reflecting pressure from Brussels for further UK concessions on a so-called "divorce bill" which could reach €60 billion.
Mrs May's official spokesman indicated that she will urge the EU27 to concentrate on the future opportunities for co-operation, rather than the details of unstitching Britain's 44-year membership.