The Supreme Court's judgement follows an appeal against the High Court's rejection of ministers' arguments.
Theresa May says the government already has powers to invoke Article 50 of the Lisbon Treaty - starting Brexit talks - by the end of March.
But campaigners say Parliament must be consulted before she does so.
Labour has already said it will not vote against the government over invoking Article 50.

With all eyes on May's general election, Carwyn Jones condemned David Cameron's Conservatives as being even more extreme than Margaret Thatcher.
He said voters had a choice between "hope and despair".
Meanwhile Labour leader Ed Miliband has launched an attack on tax avoidance for damaging the "fabric of society".
He told the conference there would be a "root and branch" review of Her Majesty's Revenue and Customs if Labour won the election, claiming the UK's tax authority had one rule for the rich and another for the poor.
In his keynote speech on Saturday, Mr Jones hailed the Welsh government's record on jobs, investment and tuition fees as evidence of what a UK Labour government could achieve.
He said the Conservatives "denigrate" the NHS in order to dismantle it, and insisted Labour's record on health in Wales was better than that of the Westminster coalition running it in England.
Mr Jones also called for a more "tolerant" society which could debate immigration with "fairness and respect", and not let "right-wing, dog-whistling xenophobes drag us down to their level".
A Â£40m scheme with the aim of helping people set up 10,000 new businesses creating 17,000 jobs over the next five years was also announced.
Unusually for the first minister, this was a speech dominated by attacks on the Tories.
He recalled the days of his political awakening during the miners' strike and said the current cutbacks were more severe than those felt in the 1980s.
He even likened the so-called bedroom tax to the poll tax.
There was some policy but basically this was a speech that acknowledged that the next few weeks is not about his government, although the Conservatives have other ideas.
Just to pick up on one comment: he took a hard line on health boards, saying he won't apologise if they fail.
This is a change of tone and I'm told it's the result of deep frustration with Betsi Cadwaldr health board in particular over the way last week's decision to move to a midwifery-led maternity unit at Ysbyty Glan Clwyd was handled.
I think we can expect more of this tone in future, as Welsh government ministers become more open in their views of health boards if they feel there are problems.

A tumultuous year in senior management, continuing into the start of this year, required revisions to the accounts.
Several directors left and the chief executive, who is scheduled to leave, is no longer receiving a bonus.
The accounts do not give detail of what went wrong, though the boardroom rows were well publicised in the media.
However, the report to Companies House indicates the company has lost out from the drop in energy prices, buying its fuel in advance of the sharp drop in oil market.
In a statement with the accounts, the directors stated: "The group has faced significant operating and cost pressures.
"We anticipate that these cost pressures will remain in 2015 and we will remain proactive in seeking to mitigate the impact of these cost pressures".
Lothian Buses revenue in 2014 was up by 2.3% to Â£135m. Pre-tax profits fell from Â£11.7m to Â£10.1m.
The company is owned mainly by City of Edinburgh Council, with small stakes held by neighbouring Lothian councils.
It owns more than 650 buses, and carries more than two million passengers each week. The numbers transported were up in 2014 by 2.6% to a total of 118 million.
The government will learn next Tuesday whether it has won its legal battle to get Brexit under way without the need for a vote by MPs.
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Only Labour can stop the Tories from decimating public services, the first minister has told the Welsh Labour conference in Swansea.
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Lothian Buses, which dominates Edinburgh public transport, including trams and tourist tours, has reported a drop in profits during last year.