Today, the Government published a paper outlining our offer for EU citizens in the UK, and UK nationals in the EU. You can read more about our offer for EU citizens on GOV.UK: Status of EU citizens in the UK: what you need to know.
You can also read the full policy paper: Safeguarding the position of EU citizens living in the UK and UK nationals living in the EU
There is no need to do anything now. The UK will remain a member of the EU until March 2019 and there will be no change to the rights and status of EU citizens living in the UK, nor UK nationals living in the EU, during this time. So, EU citizens do not need to apply for documentation confirming their status now.
Our policy paper sets out that we will be asking EU citizens to make an application to the Home Office for a residence document demonstrating their new settled status. We will make the process as streamlined and user-friendly as possible for all individuals, including those who already hold a permanent residence document under current free movement rules. We expect the new application system to be up and running in 2018.
Information is also available on what UK nationals travelling and living in Europe need to know.
Home Office Communications