It is the first meeting between the leader of the opposition and the key EU figure in Brexit talks, and comes just a day after Mr Barnier hit back at Foreign Secretary Boris Johnson for his suggestion that the EU should “go whistle” over a multi-billion financial settlement.
Mr Corbyn criticised the Tory approach to the negotiations, saying: “In contrast to the Conservatives’ megaphone diplomacy, we will conduct relations with our European neighbours respectfully and in the spirit of friendship.
“Our strong links with our European sister parties gives Labour an advantage in reaching an outcome that works for both sides”.
The Labour leader said that while “respecting the referendum result”, a “Labour Brexit” would be very different.
Mr Corbyn said the party’s approach would be to secure “a jobs-first Brexit” and one which unilaterally guarantees the rights of EU citizens currently in the UK “as it’s the right thing to do”.
However, the opposition’s position on the single market has been criticised as vague and incoherent.
During the General Election campaign Mr Corbyn backed both leaving the single market and joining the European Economic Area, which most people consider to be the same thing.
However, the party’s position did seem to paper over divides in Labour’s support during the election campaign.
Mr Corbyn sacked four shadow frontbenchers for voting in favour of a backbench motion guaranteeing single market membership.
The Labour leadership position is thought to be very sympathetic to staying in the customs union, on account of protecting jobs at key manufacturers with Europe-wide supply chains.
The Government argues this would restrict the ability to sign independent new trade deals, but will not publish evidence proving the trade from such deals would make up for any trade lost in Europe.
Labour has strong associations with sister parties in office in different EU nations. Mr Corbyn claims he can get a better deal by using these connections.
As well as meeting Mr Corbyn, Mr Barnier will also meet with the First Minister of Scotland Nicola Sturgeon and the Welsh First Minister Carwyn Jones.
The Government this week asked for cross party ideas on Brexit, a call that has been repeated by Brexit Secretary David Davis.
Speaking ahead of the publication of the Great Repeal Bill, which will copy across EU legislation into UK law, Mr Davis said he would “work with anyone” to achieve Brexit.
“By working together, in the national interest, we can ensure we have a fully functioning legal system on the day we leave the European Union,” he said.
“The eyes of the country are on us and I will work with anyone to achieve this goal and shape a new future for our country.”