Acknowledging the hard talks ahead, British Secretary for Brexit David Davis, said the talks would be held in a constructive and positive atmosphere, and would deliver a deal "that works in the best interests of all citizens".
The talks will focus on issues regarding citizens rights, the United Kingdom.
He added that an orderly withdrawal was essential for both Britain and the EU. He thought that this first round of negotiations would be about getting a feel for each other. As in any divorce, count on both sides to be picky in splitting the goods and dues.
"Northern Ireland is very complex and sensitive and we take it extremely seriously", Davis said.
Merkel spoke after meeting with Romanian President Klaus Iohannis, who also stressed the 27 European Union countries' unity.
In carefully choreographed talks that even saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start.
The talks will be in English and French, they said in a joint statement.
Only when "sufficient, concrete progress" on the first phase has been made will Mr Barnier recommend to the European Council that the negotiations can enter the next stage, taking in the future trading relationship, with that recommendation possibly coming at October's summit of EU leaders.
The letter said: "The business community fully accepts the decision of voters last June that the United Kingdom will leave the European Union". Such firms sold 7.3 billion euros ($8.2 billion) worth of goods to customers in Britain previous year, their fourth-biggest market.
Barnier said he hoped the talks, starting nearly a year to the day after a British referendum vote to leave the EU, would "identify priorities and a timetable that would allow me to report to the European Council later this week that we had a constructive opening of negotiations".
Anxious by immigration and loss of sovereignty, Britons voted a year ago to end their country's four-decade membership in the 28-country bloc - the first nation ever to do so.
The talks are set to kick off at 11 a.m. (0900 GMT) in Brussels with a meeting between Davis and the EU's chief Brexit negotiator Michel Barnier.
Significantly, Mr Davis said he would tell Labour and other parties about the Government's plans in advance - reflecting its weak position, with no Commons majority.
"Our big problem is that we have no picture, no idea at all, what the British want", said German Manfred Weber, the head of the EPP Christian Democrat group in the European Parliament.
He added: "The United Kingdom has made a decision to leave the European Union, it is not the other way around. Then in the second step we will scope our future partnership".
A year after Britons shocked the continent by voting on June 23 to cut loose from their main export market, new debate within Prime Minister Theresa May's cabinet on precisely what kind of trading relationship to pursue has perplexed European Union leaders, who warn time is tight to agree terms before Britain leaves in 2019. "This is a major event, and it's not about negotiating peanuts".
Davis said he was looking forward to starting work on crafting the new future relationship between Britain and the EU.
"The most important thing for us is to look to the horizon, raise our eyes to the horizon".