"The PM is pleased that we've made more progress in the EU negotiations and that we are able to give businesses and citizens certainty ... and will allow us to trade on the same terms as now until 2020," a spokesman for British Prime Minister Theresa May said.
Asked whether Britain had sold out, the spokesman said it was a negotiation that involved "give and take on both sides".
The issue of the border between EU member state Ireland and Britain's territory Northern Ireland is central to an agreement, but negotiators are struggling to find a way to keep people, goods and services flowing while respecting EU controls.
British Prime Minister Theresa May has described as unacceptable any possible deal that cuts Northern Ireland off from the rest of the United Kingdom by leaving the British-ruled province subject to EU rules after Brexit.
Any such deal is likely to be unpalatable to London and pro-British Unionists in the province.
Mr Davis said the transition agreement and a deal on rights for expatriate citizens would give considerable certainty to individuals and companies affected by Brexit on March 29, 2019.
Ms May's prime goal has been to secure the political accord that will now leave Britain essentially a non-voting EU member until the end of 2020 to ease concerns for business.
That accord is now likely to be endorsed by leaders of the other 27 EU member states at a summit on Friday, a day after they have met Ms May herself in Brussels.
Britain hopes to avoid Irish 'hard border'
The biggest stumbling block has been Ms May's rejection of the original draft language on Ireland issued by the EU three weeks ago.
It said that if Britain and the EU did not find any better way to avoid customs barriers and other mechanisms likely to renew tensions in Northern Ireland, then the province should follow EU economic rules even if the rest of the UK did not.
Ms 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.
Britain argues it has two other preferred outcomes for the Irish border, both dependent on agreement on future EU-UK trade rules. Negotiations on that will not start until next month, once Friday's EU summit gives Mr Barnier the go-ahead.
The Irish protocol now appears in yellow in the draft text, indicating that Britain had accepted all the EU's principles, but wanted to discuss the operational issues.
"The Brits have just given in on everything, so big was their drive to get the transition. On citizens' rights, on many other elements," an EU diplomat involved in negotiations told Reuters.
Among other issues outstanding on a text that both sides hope can be agreed by October are how the judicial process to enforce the accord will work. London is resisting EU demands for a final say for EU courts.
Financial markets welcomed the deal. The pound rose as much as 1 per cent against the dollar to $1.4088, its strongest since February 16.
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