Davis said the transition agreement and a deal on rights for expatriate citizens would give considerably certainty to individuals and companies affected by Brexit on March 29, 2019.
The biggest stumbling block remains the question of the border between the Irish Republic and Ireland when Britain leaves the European Union (EU). She did not initially say when her government would trigger Article 50 of the European Union treaty to start the two-year talks leading to Britain's formal exit.
The Democratic Unionist Party (DUP) is unconcerned by the United Kingdom government's renewed commitment to a "backstop" solution avoiding a hard border post-Brexit, a party source has said.
He said they had agreed that the EU's "back stop position" which would see Northern Ireland effectively remain part of the single market if there was no wider agreement, would form part of the legal text of the withdrawal agreement.
Update 7.59am: Tánaiste Simon Coveney is expected to warn today the Brexit negotiations can not move on unless Britain signs off this week on the backstop deal to ensure there is no hard border when it leaves the EU.
Sterling was trading up 0.7% against the euro at 1.14 euros.
The UK's Brexit Secretary David Davis and the EU's chief negotiator Michel Barnier both say that agreement has been struck on arrangements for a transition period after Britain's departure from the bloc in March 2019.
Firms across Europe that need to plan their business years in the future have been clamouring for both sides to reach a deal to avoid a cliff-edge departure, and Davis said it was "near enough" the full two years Britain had demanded.
"Some food and drink businesses will be ready earlier than two years but transition must not end until the bulk of the industry is ready and we have confidence in the systems on both sides of the Channel".
"The European Parliament's Brexit Steering Group welcomes the political agreement, in principle, of a transition period, although we reserve our right of scrutiny".
One sticking point that could unravel the agreement is the issue of the border between the Republic of Ireland, which is, and will remain a part of the European Union and Northern Ireland, which is part of the UK.
"She is not being asked to agree to the backstop but more to the principle that there has to be a backstop", said one European Union source.
May, who depends on Northern Irish votes for her slender parliamentary majority, said no British prime minister could ever agree to such an isolation of the province from the mainland. No agreement on the right operational approach but we know what we need to do.
"The agreement between the EU and UK on a transitional period up until December 2020 is welcome news particularly in relation to continued frictionless trade across UK-EU borders for the transition".
But Scottish Tory MP Douglas Ross said: "There is no spinning this as a good outcome, it would be easier to get someone to drink a pint of cold sick than try to sell this as a success".
The UK insists that despite accepting that a back stop will be included in the final withdrawal agreement, it has not accepted the current wording proposed by the EU.
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