"The deal on what the UK calls the implementation period was a "decisive step" in the Brexit process", Negotiators Michel Barnier and David Davis said.
But issues still to be resolved include the Northern Ireland border.
And Scotland's fishing industry has reacted angrily to the deal, which will see the UK "consulted" on quotas and access to its waters until 2021.
Brexit Secretary Mr Davis said Monday's transition agreement, which is conditional on both sides agreeing a final withdrawal treaty, would smooth the path to a future permanent relationship.
Barnier said the legal text marked a "decisive step" but added that it was "not the end of the road".
The key aspects of the agreement announced in Brussels are:
The transitional period will last from Brexit day on 29 March 2019 to 31 December 2020
EU citizens arriving in the UK between these two dates will enjoy the same rights and guarantees as those who arrive before Brexit. The same will apply to UK expats on the continent
Northern Ireland will effectively stay in parts of the single market and the customs union in the absence of other solutions to avoid a hard border with the Republic of Ireland
Both the UK and the EU hope the terms of an agreement on the transitional period can be signed off by Mrs May's fellow 27 leaders at the EU summit this week.
The UK citizens are less optimistic about Brexit, with the gap between the supporters and opponents of the country's withdrawal from the European Union reaching 10 percent, a fresh poll showed on Sunday.
According to a poll by BMG Research for the Independent newspaper, 41 percent of the UK citizens support Brexit, while 51 percent believe that the country should remain in the bloc.
