Dominic Raab was appointed when David Davis resigned in protest at Theresa May’s plans for post-Brexit trade.
It now falls to Mr Raab – part of the winning Leave campaign in the 2016 EU referendum – to continue negotiations with the EU’s Michel Barnier.
Their meeting comes as the European Commission is instructing other EU states to prepare for a no-deal Brexit.
The BBC has seen a draft of a commission paper which warns that failure to reach a deal would have a considerable impact on European business and citizens.
Possible consequences, the paper says, include disruption to the aviation industry and goods from the UK being subject to custom checks.
Taoiseach (Irish prime minister) Leo Varadkar has said his government is making contingency plans for “the unlikely event of a no-deal hard Brexit”.
Mr Varadkar said that – even if there is a deal – Ireland will need 1,000 new customs officers and veterinary inspectors to deal with changes in trade rules with the UK.
In the UK, the government has advised all its departments to have fully planned contingencies in place in the event of the UK withdrawing from the EU without an agreement.
However the government watchdog, the National Audit Office, has warned that, in the case of one department, there is “still much to do”.
On Thursday, Theresa May will be making her first visit to the Irish border since the Brexit referendum.
No 10 says the visit will “reaffirm her commitment to a Brexit that avoids a hard border and protects the Belfast Agreement”.
The UK is due to leave the EU on 29 March 2019.
But the two sides have yet to agree how their final relationship will work, with key issues around cross-border trade unresolved.
Mr Raab’s trip to Brussels comes with debate raging within the Conservative Party about what Brexit should look like.
A baptism of fire
By Katya Adler, the BBC’s Europe Editor
It will be quite a baptism of fire for the new Brexit secretary.
He will be greeted here in Brussels with a barrage of questions.
First and foremost amid all the political turmoil in Westminster: What exactly is the UK’s Brexit negotiating position now?
The EU also has a strong message for Dominic Raab.
Work with us, they will say, to finish the UK’s exit deal – the so-called Withdrawal Agreement – otherwise the chances are rising of the UK crashing out of the EU without a deal come March next year.
On Wednesday, former Foreign Secretary Boris Johnson – who also quit over the proposals presented to the cabinet at Chequers – used his resignation speech to accuse Theresa May of “dithering” over the UK’s strategy for leaving the EU.
“It is not too late to save Brexit”, he said, calling for the government to “change tack”.
Former Remain supporters, on the other hand, were furious when the government changed its Customs Bill this week to comply with the demands of a Eurosceptic group of Tory MPs.
The EU says it will analyse the Chequers proposals, which were set out in full in a White Paper, before coming up with a response.
Speaking in the House of Commons on Wednesday, Mr Raab urged MPs to back Theresa May’s plans.
He said: “What we now should all do on all sides of this chamber is not call for second referendums, not call for returning to the customs union, but get behind the government’s plan, show some united front, so we get the very best deal for everyone in this country.”