He said it was "very clear" his party accepted the referendum result.
Some shadow cabinet members are reportedly considering voting against triggering the UK's EU exit negotiations.
The Supreme Court will announce next Tuesday whether the government needs to seek Parliament's approval.
Ministers say they already have enough powers under the Royal Prerogative to go ahead with Brexit.
But campaigners argue that starting Brexit in this way would be undemocratic and unconstitutional.
In June's referendum, 51.9% of voters backed leaving the EU, while 48.1% supported remaining in the 28-nation group.
Mr Corbyn said: "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 - the strongest available sanction - 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 Guardian reports that four shadow cabinet ministers and several junior Labour spokespeople were considering defying Mr Corbyn and voting against Article 50 being invoked.
The Supreme Court's decision on whether a vote needs to take place follows a government appeal against a High Court ruling last autumn that MPs and peers should have to vote give their approval.
Following Mr Corbyn's comments, Green Party co-leader Caroline  Lucas said he was "trying to deny Labour MPs the chance to make their own principled choice on one of the most important decisions of the UK's recent history".
And Liberal Democrat leader Tim Farron said Mr Corbyn was "actively helping" the government in its plans to leave the European single market, "at a huge cost to jobs and prosperity".

The North Wales Health Alliance (NWHA) said a Betsi Cadwaladr University Health Board report highlighted serious issues around patient safety.
The pressure group said it meant, in some cases, the board risked breaking the law.
The board said it was already working on measures to reduce risks.
The findings of the annual safeguarding report were presented to officials at the health board last week.
It outlined 13 'red' areas of risk, including:
The concerns by the NWHA come as the board meets on Thursday to get the latest update on two inquiries into events at Glan Clwyd Hospital's Tawel Fan ward, which closed in 2013.
"A year and a half after going into special measures and receiving additional support, we have to ask whether Betsi Cadwaladr is learning lessons and making improvements?" stated Marc Jones, from the NWHA.
"These are not trivial issues but are serious risks. The scandal surrounding Tawel Fan should have been a wake-up call regarding the need to take at-risk patients' safety and well-being seriously.
"We do not want to see a repeat of that."
The health board's own analysis of its safeguarding weaknesses highlighted "unclear" policies, little evidence of sharing good practice, and relatively low uptake on safeguarding training.
In an independent investigation in May 2015, relatives said patients on the Tawel Fan ward were treated like animals in a zoo.
It led to the health board being put into special measures by the Welsh Government, and its former chief executive stepped down.
Betsi Cadwaladr board members will be told later that the current inquires into what happened are expected to continue until the summer.
Responding to the NWHA criticism, Dr Evan Moore, the board's executive medical director, said "positive action" was already under way and have continued since the safeguarding assessment was made in autumn 2016.
"The committee recognised that these had lowered our exposure to the risks in many areas and as a result agreed that the associated risk scores would be reduced.
"The board will consider a detailed report on this in public at its full meeting in March."
Jeremy Corbyn says he will ask his MPs to vote for the Article 50 Brexit process to begin, if the government is forced to seek Parliament's approval.
[NEXT_CONCEPT]
Campaigners have accused a health board of risking patient safety and failing to learn lessons from a mental health ward scandal.