"The most important thing I think now is for us to think about the new partnership, the deep and special partnership that we want to build with our friends", said Johnson, who campaigned in last year's referendum to leave the EU.
"Michel and I will meet every four weeks bringing our teams together for a number of days at a time".
Day One of the negotiations will be followed by a joint press conference later by Davis and Barnier. "We must first tackle the uncertainties caused by Brexit", centering on citizens living on each other's territory, border arrangements between Ireland and the United Kingdom and the amount that Britain stands to pay to get out of its previous European Union commitments, Barnier said. There's a long way to go but we're off to a promising start.
A member of protocol changes the EU and British flags prior to the arrival of EU Chief Brexit Negotiator Michel Barnier and British Secretary of State David Davis at EU headquarters in Brussels on Monday, June 19, 2017.
The EU has said that before it will start discussing a future trade deal with the United Kingdom, it wants to resolve the biggest uncertainties arising from Brexit, including the future rights of around 3 million EU citizens in the United Kingdom and the arrangements for avoiding a hard border between Northern Ireland and the Republic of Ireland.
According to Barnier, the intention on behalf of the European Commission is to keep talks as transparent as possible.
David denied any retreat by his government, noting that "both sets of dialogue will continue once the European Union 27 will agree that divorce talks have reached "sufficient progress".
Describing the negotiation as exceptional, Barnier denied to give further details on how he will secure the transparency of talks. European Union diplomats hope this first meeting, and a Brussels summit on Thursday and Friday where May will encounter - but not negotiate with - fellow European Union leaders, can improve the atmosphere after some spiky exchanges.
Despite tweeting he's under investigation, Trump lawyer says he's not under investigation
He says there should at least be tapes of any telephone conversations between the president and Comey. The Post cited multiple unnamed sources familiar with those interview requests.
Three working groups have been set up, on citizens' rights, the financial settlement, and other "separation" issues.
Austrian Foreign Minister Sebastian Kurz said: "If we don't succeed both sides will lose". They also exchanged gifts that recognised their shared passion for hillwalking and the uphill task ahead: a hiking stick for Mr Davis, and a book on hiking for Mr Barnier.
She had hoped to strengthen her government's hand in the negotiations by holding a snap election this month and solidifying the hold of her Conservative Party on the parliament.
Mr Barnier said a "fair deal" was possible "and far better than no deal" and promised to work with, not against, the UK.
In addition to the one-day talks, British Prime Minister Theresa May will be in Brussels later in the week for an EU Council summit.
"An optimist sees the opportunity in every difficulty".
He quoted the founder of the trading bloc that later became the European Union, Jean Monnet, as saying: "I am neither optimistic nor pessimistic".
If Britain crashes out of the European Union without a deal, that would create huge uncertainties for citizens and businesses as well as issues like global security.
Comments