The agreement was signed earlier in the day in the Swiss city of Bern by UK Secretary of State for International Trade Liam Fox and Swiss Federal Councillor Guy Parmelin.
The UK is set to sign an agreement with Switzerland on Monday to continue trading on preferential terms after Brexit, protecting a trade relationship worth £32bn ($41.4bn).
Britain has long traded around the world under the terms of deals agreed by the European Union, a procedure that will come to an end after Brexit.
Opponents of a no-deal Brexit inside her cabinet and on the Tory backbenches want to hear confirmation from the prime minister that any motion she tables then will be amendable.
Mr Johnson accused Mr Corbyn of trying to "frustrate" Brexit by demanding a customs union, which he said would prevent the United Kingdom from striking its own trade deals.
"I'm certain of one thing, is that it's not going to be as good as if they had not been Brexit, that is for sure", Lagarde said.
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The impasse has left the world's fifth largest economy facing an uncertain future, rattling financial markets and businesses about the prospect of a disorderly exit from the bloc that could damage the economy.
The Swiss government is pursuing a strategy dubbed "Mind the Gap", which is meant to stabilise British ties after Brexit.
Brexit minister Stephen Barclay will meet European Union negotiator Michel Barnier on Monday to discuss changes to the part of the exit deal relating to the "backstop", an insurance policy against the return of a hard border between European Union member Ireland and British-ruled Northern Ireland. It covers issues like free trade, public procurement, agriculture and the fight against fraud.
A customs union is one of the demands made for any deal to get Labour support.
The deal will also apply to Liechtenstein - represented by foreign minister Aurelia Frick - under the Swiss-Liechtenstein Customs Union. He says May's agreement can achieve "a great deal of what Jeremy Corbyn is interested in without taking away that option of having other trade deals".
"We have got what we call the Political Commission that simply does not take its orders from democratically elected governments".
He told the Sunday Times he fears the Prime Minister is "pretending to make progress" but actually intends to return to Parliament after the March 21/22 European Council summit the week before Brexit and offer MPs a "binary choice" - her deal or no deal.