In a significant policy shift, Mr Corbyn will call for Britain to retain “a strong relationship with the single market” after Brexit in March 2019.
The move raises the prospect of the government having to change its own position on Brexit or risk losing parliamentary votes on bills due to be put before MPs in the coming months.
Pro-EU Tory MPs are already planning a series of amendments aimed at keeping Britain in a customs union. Labour support for the position raises the prospect of the government losing the vote or having to change its stance.
Some Conservatives have raised the prospect of the government collapsing if the Prime Minister loses votes on trade and customs bills due to be heard, the Financial Times reported.
Brexit Secretary David Davis said Mr Corbyn’s plans breached the promises he made at the general election and accused him of selling “snake oil”.
In a speech in Coventry on Monday, Mr Corbyn will say: “Every country that is geographically close to the EU without being an EU member state, whether it’s Turkey, Switzerland, or Norway, has some sort of close relationship to the EU, some more advantageous than others.
“Britain will need a bespoke relationship of its own. Labour would negotiate a new and strong relationship with the single market that includes full tariff-free access and a floor under existing rights, standards and protections.”
But Mr Corbyn is expected to set out how Labour would commit to the UK being part of a customs union.
Labour has had “many weeks of discussion unanimously” and agreed to develop its policy, shadow Brexit secretary Sir Keir Starmer said.
“The customs arrangements at the moment are hardwired into the membership treaty so I think everybody now recognises there’s going to have to be a new treaty – it will do the work of the customs union,” he told BBC One’s The Andrew Marr Show.
Prime Minister Theresa May has ruled out membership of the single market or customs union after Brexit, a move that has angered Tory Remainers.