Mr. Corbyn and Scottish First Minister Nicola Sturgeon will meet Mr. Barnier separately on Thursday, as will Wales' First Minister, Carwyn Jones, amid criticism from some who see it as a snub to the British Prime Minister Theresa May.
The second round of Brexit negotiations is due to begin on Monday, July 17, and Mr. Barnier has said the rights of EU citizens in Britain, and British citizens' rights in EU countries, will be top of the agenda.
Mr. Corbyn, who has repeatedly said he is a "prime minister in waiting," will "outline" his party's position on Brexit, which is considerably "softer" than the hard Brexit favored by Mrs. Mayand her allies in the Democratic Unionist Party.
The Labour leader wants to see guarantees on the rights of EU citizens in the UK and is also keen to avoid Britain becoming an "offshore tax haven on the shores of Europe."
He tweeted he was in Brussels to set out Labour's priorities for a "jobs-first Brexit."
There's no such thing as "a jobs-first Brexit" Jeremy. If you value jobs, you need to work to stop Brexit.— Alexander Coles (@ajcoles) July 13, 2017
But the Tories have claimed Mr. Corbyn would "surrender" to the EU, rather than stand up to them in the Brexit negotiations.
On Wednesday, July 12, Mr. Barnier briefed European commissioners on the British government's proposal on the rights of the 3.2 million EU citizens who live in the UK, which includes 800,000 Poles.
Mrs. May's government published the European Union (Withdrawal) Bill on Thursday morning, which is better known as the Repeal Bill.
But Labour has already warned it will vote against it unless it is significantly modified.
"This will be hell," warned the Liberal Democrats outgoing leader Tim Farron.
The bill will ensure existing EU legislation applies in Britain after Brexit, while giving Parliament the power to change it.
Labour said it would guarantee EU nationals' rights in Britain, without waiting for a reciprocal offer from Brussels.
"In contrast to the Conservatives' megaphone diplomacy, we will conduct relations with our European neighbors respectfully and in the spirit of friendship," Mr. Corbyn said.
"Our strong links with our European sister parties gives Labour an advantage in reaching an outcome that works for both sides," he added.
His invitation to Brussels comes hours after Foreign Secretary Boris Johnson said the EU could "go whistle" if it tried to demand a lot of money from the UK as part of the Brexit divorce.
"I'm not hearing any whistling, just the clock ticking," Mr. Barnier responded ominously.
Boris Johnson said we can "go whistle for our money". I agree with Michel Barnier. We need to settle the accounts and the clock is ticking.— Guy Verhofstadt (@GuyVerhofstadt) July 12, 2017