"Labour respects the decision of the British people to leave the European Union," the Labour Party leader said in a statement.
"But there must be transparency and accountability to parliament on the terms of Brexit."
On Thursday morning, the British High Court ruled that British Prime Minister Theresa May must get Parliamentary approval to trigger Article 50, which kick starts the two-year formal negotiation process for Britain leaving the EU.
The ruling Conservative government has insisted that it has the authority to begin Brexit without parliamentary approval, and immediately said it plans to appeal - sending the battle to the Supreme Court, Britain's highest court.
Some Remain-supporters have viewed the legal case as a chance to delay or even block Brexit entirely - despite the June referendum results. And the majority of MPs (from both Labour and the Conservatives) were pro-Remain, raising the possibility that they could vote to derail Brexit.
But Jeremy Corbyn says that the Labour Party will respect the referendum result, and will focus on getting the best deal possible for Britain if the government's appeal fails.
"This ruling underlines the need for the government to bring its negotiating terms to parliament without delay. Labour respects the decision of the British people to leave the European Union. But there must be transparency and accountability to parliament on the terms of Brexit," he said in a statement.
"Labour will be pressing the case for a Brexit that works for Britain, putting jobs, living standards and the economy first."
However, given Corbyn's acrimonious relationship with many of his parliamentary colleagues, there's no guarantee that they would vote to trigger Article 50, even if ordered to do so.