Solving the vexed question of keeping the peace and an open border between the United Kingdom province of Northern Ireland and the Irish Republic will also be an urgent priority in the talks, Barnier and Davis agreed.
"We agreed on dates, organisation, and we agreed on priorities for the negotiations", Barnier said at a joint press conference with Davis.
Ireland has been part of the European Union since 1973 and has had a free-flowing border with Northern Ireland since the Good Friday Agreement in 1998 that ended 30 years of sectarian violence in Northern Ireland, known as "The Troubles".
Finance minister Philip Hammond confirmed Sunday that it was still the plan to quit not only the EU but the customs union and the bloc's single market as well. "And the consequences are substantial".
A detailed paper will then be published on Monday, Mr Davis confirmed. "And use the time in between to work on proposals and exchange them".
Davis and Barnier have one key issue over the first weeks of talks: building trust after months of haggling over leaks and figures over the final bill that Britain would have to pay for leaving.
Still, British Foreign Secretary Boris Johnson remained upbeat on Monday and thinks that the Brexit negotiations will yield "a happy resolution that can be done with profit and honor for both sides".
"So now that the negotiations have started, we are determined to get on with the job and deliver that certainty as soon as possible".
The announcement was made alongside the start of discussions with the European Union on Brexit on June 19.
"So what we're seeing is a big debate about economics versus identity, and the Government's going to have to try and tread what is a very rocky road".
But many in Brussels fear that London has no real strategy, with May under pressure at home and still trying to close a deal with a conservative Northern Ireland party to stay in power, and facing criticism for her handling of the aftermath of a devastating tower block fire.
Davis's agreement to Monday's agenda led some European Union officials to believe that May's government may at last coming around to Brussels' view of how negotiations should be run.
Ian Murray, the Labour MP for Edinburgh South, called on Mr Davis to abandon any suggestion that the United Kingdom could walk away from Brexit talks without a deal.
But in Britain many media portrayed Davis, a veteran Brexit campaigner, as having climbed down from his insistence that the European Union must immediately open talks on a future free trade agreement rather than limit negotiations, as they are now, to basic issues of the divorce, such as the rights of expatriate citizens.
Anthony Martial has completely shut down all rumours that his representatives have discussed an exit from Manchester United . Alongside the written message, Martial included a red emoji - reaffirming his commitment to United.
Dawid Malan was named man of the match after making the highest score by an England player on their T20 debut. AB de Villiers believes South Africa's excellent Test record in England will work in their favour again.
Borrowers often do everything they can to pay off mortgages , but are less afraid about defaulting on credit cards or auto loans. The Bank's assessment said loss rates on consumer lending "are low at present", driving margins on new lending lower.
LSU - playing its fourth game in six days and with Eric Walker out with an injury - turned to the seldom-used Reynolds to start. The Gators had eight players drafted in the first 10 rounds of last year;s Major League Baseball draft but went 0-2 in Omaha.
There were some slight winners like Charlotte and Utah landing Malik Monk & Donovan Mitchell respectively at surprising spots. Fast food probably isn't a deal-breaker when it comes to where you play in the National Basketball Association .
He told them that the experience will be better on PC, and that Xbox is choosing to focus on mixed reality or augmented reality. Spencer's comment does make sense in the perspective that the Xbox One X offers specifications that Sony can't now rival.
Tillerson said that "a productive next step would be for each of the countries to sit together and continue this conversation". Bahrain, Saudi Arabia, United Arab Emirates (UAE) and Egypt have cut ties with Qatar on terrorism funding charges.
In 2012, President Obama famously warned that the use of chemical weapons use would constitute a red line , triggering US action. Days later, President Donald Trump ordered a retaliatory cruise missile strike on a Syrian government-controlled air base.
Sporadic sniper fire could be heard, and an incoming rocket, as the troops used a drone to survey the insurgents' defences. Islamic State has lost about half the Old City since the battle for the historic district started ten days ago.
Trump bested Democrat Hillary Clinton in Iowa by almost 10 percentage points in the election previous year . On the border wall, the president reassured his base: "And yes, we will build the wall".
Oil price extends drop to 7 month lows, despite OPEC cuts
This, combined with the hostile political climate in North Africa and West Asia has threatened exports, causing the supply glut. The Iranian minister spoke highly of OPEC's performance in arriving at a consensus to cut output and help prop up prices.
New Analyst Ratings For Morgan Sindall Group (LON:MGNS)
In related news, insider Steve Crummett sold 13,174 shares of Morgan Sindall Group PLC stock in a transaction on Friday, May 19th. Winslow Evans Crocker accumulated 4,380 shares or 0% of the stock. 435,528 shares of the company's stock traded hands.
Modi meets Trump with his usual greeting _ bear hugs
These energy contracts "are being negotiated and we will sign - trying to get the price up a little bit", Trump said . India and the USA also urged Pakistan to ensure that its territory is not used to launch cross-border terror strikes.
Cosby Jury Goes Over Accuser's Testimony During Deliberations
Last week, Pulliam gave a similar statement to ET, again making it clear that she doesn't "condone or support sexual assault". Prosecutors have portrayed Cosby as a serial predator. "A 30-year consecutive sentence would be a life sentence", she said.
Co-op Bank agrees 700 million pound rescue package
The Co-operative Bank has secured £700m of funding to meet regulatory capital requirements, staving off a once-mooted sale. The bank added that the Bank of England's Prudential Regulation Authority supported the rescue plan.
Cosby trial accuser thanks supporters for love, kindness
Cosby stemming from other possible victims, his defense attorney said "None of these accusations have ever been vetted". I'm not going to plea to something I did not do", Cosby said, during an exclusive interview with the NNPA Newswire.
Former NBA bad boy Rodman is back in North Korea
The announcement comes as former National Basketball Association player Dennis Rodman is paying a return visit to North Korea . Warmbier also said he had been encouraged by the university's "Z Society", which he said he was trying to join.
IS counterattacks in retaken parts of Mosul stall Iraq push
Baghdadi has left the fighting in Mosul to local commanders and has been assumed to be hiding in the Iraqi-Syrian border area. An Islamic State (IS) suicide bomber has blown himself up during a meeting in Mosul that also killed a number of commanders.
EU Fines Google $2.7 Billion
A 7-year investigation by the European Commission concludes that the search engine benefited from an "illegal advantage". The company will review the decision and consider an appeal.