Britain also agreed in principle to the EU's "backstop" plan for the status of the Irish border, under which British-ruled Northern Ireland would remain part of the EU's Customs union if there is no better idea.
The Irish backstop, while crucial for securing the transition deal, may cost London dearly if no other solutions are found.
"But it remains our intention to achieve a partnership that is so close as to not require specific measures in relation to Northern Ireland and therefore we will be engaged in detail on all the scenarios set out in the joint report", he stated.
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Barnier said that once the deal was given the green light by the European Council negotiations between the two sides could quickly commence, adding that formal trade negotiations with the United Kingdom could only start once it was a third country.
The Confederation of British Business (CBI), which represents the country's biggest companies, said the breakthrough had brought a welcome gift for firms on both sides and had helped lift a cloud of uncertainty for businesses.
Tony Blair's former chief of staff warned that a return to "huge concrete slabs" and "checkpoints on the main roads" could "force Northern Ireland back into identity politics".
Foreign Minister Simon Coveney, who met Barnier in Brussels before the announcements on Monday, said he was satisfied: "Good progress today on Brexit", he tweeted, thanking Barnier and Davis.
The pound rose as much as 1 percent against the dollar to $1.4088, its strongest since February 16.
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With the event still ongoing, I sat down with an Epic Games representative to discuss the game's new home and its appeal. As a Pro Fortnite Buddy, you can earn at least 30 British Pounds per hour, which equals to over 41 American Dollars .
Sterling climbed to $1.41 against the dollar and reached 87 pence against the euro on news of the deal. "Legal certainty is what counts". Those deals would then take effect once Britain was free to do so in 2021.
In a piece of choreography agreed with the EU27, Mrs May published an open letter to European Council President Donald Tusk tonight in which she commits to turning the December agreement backstop into legal treaty terms.
Brexit negotiators Michel Barnier for the European Union, and the UK's David Davis, revealed the 130-page transition deal document at a press conference on Monday, local time.
May, who reached an outline deal on the divorce with the European Union in December, said in a statement that the deal showed that "we can get an arrangement for the future which will be in the interests" of both sides.
Agreeing transition is a critical milestone that will provide many hundreds of businesses with the confidence to put their contingency planning on hold and keep investing in the UK.
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But independent election monitoring group Golos reported irregularities during polling day, BBC News reported. But employees of state and private companies, as well as students, reported coming under pressure to vote.