Corbyn's speech coincides with results of a survey published today that found 94 per cent of respondents unsatisfied with government's handling of their Brexit concerns.
"Labour would seek to negotiate a new comprehensive UK-EU customs union to ensure that there are no tariffs with Europe and to help avoid any need whatsoever for a hard border in Northern Ireland", Corbyn told an audience in Coventry, central England.
The Confederation of British Industry, Britain's big business lobby, has also called for a customs union with the EU.
"Both the USA and China have weaker standards and regulations that would risk dragging Britain into a race to the bottom on vital protections and rights at work", he claimed - although the European Union has already negotiated several trade agreements with countries where standards and worker protections are poor already, such as Communist regime in Vietnam and the Moroccan dictatorship.
The former UKIP leader and vocal Brexit advocate was appearing on Channel 5's "The Wright Stuff", when he said that only another vote would silence "moaning" politicians and critics - and finally draw a line under the UK's withdrawal from the European Union.
"I welcome Jeremy Corbyn's announcement". The UK would be a "full and equal member" of a customs agreement with the EU.
Labour's new position, seen as opting for a "soft Brexit", poses a challenge in parliament, which is now discussing a bill to withdraw from the EU.
Greer was also critical of what he says is Labour's "continuing have-your-cake-and-eat-it approach to Brexit: "They claim a Labour government would cherry-pick benefits of the Single Market despite the EU's clear and sustained objection to any cherry-picking".
"Second, on party politics, how will Labour persuade Tory rebels to go against the Conservative Party manifesto and vote down their government, which would plunge the Tories into the greatest crisis since the split over the Corn Laws in the mid-nineteenth century?"
The leader of Britain's opposition Labour Party, Jeremy Corbyn, will clarify the party's position on Brexit on Monday in a move that could lead to a major parliamentary defeat for Prime Minister Theresa May. "If you're part of the customs union you will not be involved in that".
The left-winger, who advocates a radical programme of nationalisations and public spending, said his priority was "to get the best deal for people's jobs, living standards and the economy".
Equally, it is possible to be a member of the single market but not a member of the customs union, so when the question is raised that we will be a member of "a" customs union it seems to suggest that there will have to be a separate negotiated agreement between the United Kingdom and the EU that would ensure common external tariffs post Brexit - and that would be distinct from other arrangements of that kind that already exist.
On immigration, Mr Corbyn said free movement would end as a "statement of fact" after Brexit and committed to the "reasonable management of migration".