Posted: Wed Mar 7, 2018 5:23am
Just to add to the excellent summary by Kelvin, and to give some boring detail, the UK/EU have agreed to continue the rights detailed in Directive 2004/38/EC at Article 7(1)(a) – (c):
Article 7
Right of residence for more than three months
1. All Union citizens shall have the right of residence on the territory of another Member State for a period of longer than three months if they:
(a) are workers or self-employed persons in the host Member State; or
(b) have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State during their period of residence and have comprehensive sickness insurance cover in the host Member State; or
(c) – are enrolled at a private or public establishment, accredited or financed by the host Member State on the basis of its legislation or administrative practice, for the principal purpose of following a course of study, including vocational training; and
– have comprehensive sickness insurance cover in the host Member State and assure the relevant national authority, by means of a declaration or by such equivalent means as they may choose, that they have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State during their period of residence
But bear in mind that it's an all or nothing agreement. If negotiations can't reach agreement on a total package, then all the points that have already been agreed will be nullified.
Conclusion: make sure you're legally resident and keep your fingers crossed on a final agreement being reached!