Forged during 17 months of tough negotiations, the withdrawal agreement covers financial matters, citizens’ rights, Northern Ireland and arrangements for a 21-month post-Brexit transition phase.
A short political declaration that accompanied the text set out hopes for future security and trade ties.
But it is not the final stage, as the House of Commons in London must still approve the deal – and many MPs have warned they will not back it.
Until the agreement is approved, all sides are still planning for the potentially disastrous possibility that Britain leaves the EU with no new arrangements in place.
Media reports in London on Sunday suggested some of May’s own ministers were secretly working with EU diplomats on a “Plan B” in case parliament rejected the agreement next month.
But Austrian chancellor Sebastian Kurz, whose country holds the rotating EU presidency, said: “It is important that everyone in the UK is aware that the result that is now available is the result.
“It will certainly not be renegotiated and there will be no further room for manoeuvre.”
Dutch prime minister Mark Rutte added: “Overall, I think this is the max that we can all do, both Theresa May and her government as well as the European Union.
“No victors here today, nobody winning, we’re all losing – but given that context, this (agreement) is acceptable.”