The two chief negotiators, Michel Barnier of the European Union and David Davis from Britain, immediately set off to find common ground in their working relationship, an important touchstone to see how amicable the biggest political divorce in decades will become.
Only once the EU27 determine that "sufficient progress" has been made on these issues will talks be able to progress to a second phase, where the two sides will begin to scope out the future of their relationship.
Davis said the talks were off to a "promising start" and denied that Britain had caved in on the sequencing of the talks.
Brexit negotiators will discuss Monday Britain's financial obligations to the European Union as the long, complicated and potentially perilous process of the United Kingdom leaving the bloc finally gets underway.
This first meeting will last just a day with a joint news conference expected by both Mr Davis and Mr Barnier when they emerge. "That will be in our mutual interest, but we 27 will formulate our interests very clearly and hopefully together".
In Berlin, German Chancellor Angela Merkel emphasised the unity of the remaining 27 European Union countries, who have been alarmed in recent weeks by May's threats to walk out of the talks.
According to British media, the negotiations would focus on exit terms before deciding the future relations.
Last year's Brexit vote came as a profound shock to Brussels against a backdrop of rising anti-EU sentiment, with many - including now US President Donald Trump - predicting the bloc's eventual break-up. This is likely to be driven by politics as much as by maths, with numerous voices in the United Kingdom arguing that Britain owes the European Union nothing. Such firms sold 7.3 billion euros ($8.2 billion) worth of goods to customers in Britain past year, their fourth-biggest market.More news: Opposition's views taken into account in picking Ram Nath Kovind
The Brexit Secretary had wanted the talks to take place in parallel with negotiations on the divorce from Brussels but has now accepted the timetable set out by the EU's chief negotiator Michel Barnier.
However, European officials have said in recent days negotiations must proceed on the basis of Mrs.
From the Brexit brigade's initial chest-beating and wild promises of reduced immigration and increased prosperity to Theresa May's shrill denunciation of the EU's "threats against Britain", the British position has been chaotic and weak.
May had promised to take Britain completely out of the bloc's common trading area and slash the number of people coming from the EU.
Britain and the European Union began their first formal Brexit negotiations Monday, under pressure to seal a deal amid disarray in London over whether to go for a hard or soft divorce.
After seven hours of talks in Brussels, Mr Davis, who had previously promised the "row of the summer" over the timetable for the negotiations, remained upbeat.
"The most important thing I think now is for us to look to the horizon, think about the future, and think about the new partnership, the deep and special partnership that we want to build with our friends".