Jeremy Corbyn will order Labour MPs to vote in favour of starting the Brexit process if the Prime Minister is forced to seek the approval of Parliament to trigger Article 50.
The Labour leader said he had made it "very clear" that his party accepts the decision made by the public in the referendum.
Mr Corbyn's commitment to back Article 50 follows reports that members of the shadow cabinet were considering voting against allowing Theresa May to formally start the Brexit process.
The Guardian reported that four shadow cabinet ministers and several junior frontbenchers were agonising about the prospect of backing the measure.
But Mr Corbyn told Sky News: "It's very clear the referendum made a decision that Britain is to leave the European Union. It was not to destroy jobs and living standards or communities, but it was to leave the European Union and have a different relationship in the future.
"I have made it very clear that the Labour Party accepts and respects the decision of the British people. We will not block Article 50."
Asked if that meant he would be imposing a three-line whip on Labour MPs, requiring them to back Article 50, he said: "It means that all Labour MPs will be asked to vote in that direction next week or whenever the vote comes up."
The Supreme Court will give its judgment next week on whether the Government needs to seek the approval of MPs and peers before the formal Article 50 Brexit process begins.
The highest court in the land will decide whether to reject or allow a Government appeal against a High Court ruling which blocked the royal prerogative being used to trigger Britain's exit from the European Union without Parliament having a say.
Liberal Democrat leader Tim Farron said: "Not only did Jeremy Corbyn fail to campaign against Brexit in the referendum, he is now actively helping Liam Fox, Boris Johnson and David Davis to pull Britain out of the single market at a huge cost to jobs and prosperity.
"How can you profess to stand up for worker rights when you are conniving in a policy that will costs vast numbers of jobs? This shows that the Liberal Democrats are not only the real opposition to the Conservative Brexit government, we are now the only opposition."