The government's appeal against the High Court ruling
that MPs must vote on triggering Brexit will be heard in the
Supreme Court from 5 December.
It will last four days, with the decision expected in the new
year.
Theresa May has said she is "clear" she expects to start talks
on leaving the EU as planned by the end of March.
Campaigners say MPs and peers have to scrutinise the
government's plans beforehand, but ministers say they can decide
without this happening.
The High Court ruled last Thursday that Parliament should have a
say before the UK invokes Article 50 of the Lisbon Treaty - which
triggers up to two years of formal EU withdrawal talks.
Labour has said it will not attempt to delay or scupper this
process if a vote goes ahead but pressure is mounting on the
government from the devolved legislatures.
The Scottish government is pressing for the Holyrood Parliament
to be given a binding vote on Article 50 and will seek to oppose
the UK government as it makes the case for its own involvement in
the decision.
The Welsh government has also said it intends to intervene in
the appeal process to clarify the implications of the judgement for
the future of devolution in Wales and the respective powers of the
UK executive and the Welsh Assembly.
And Northern Ireland's top lawyer has said a separate legal
challenge to Brexit should "leapfrog" the usual legal process and
go directly to the Supreme Court.
The government said it was going to appeal almost as soon as the
ruling came out and the Supreme Court has now granted permission -
pushing through the process at a far faster pace than usual because
of the importance of the case.
After Lord Toulson's retirement this summer, the appeal will be
heard by all 11 remaining Supreme Court justices, led by their
President Lord Neuberger.
At the completion of legal submissions, the justices will
reserve their decision to a date "probably in the new year", a
spokesman for the court said.
He added: "The Supreme Court will sit in its largest courtroom
and make available a live video feed in the other two courtrooms in
the building to enable as many members of the public as possible to
observe proceedings.
"It should be added that, as with all Supreme Court proceedings,
this appeal will be live streamed on our website, so it is not
necessary for people to attend the building in person to watch the
hearing."
On Monday, Mrs May said: "We believe the government has got
strong legal arguments. We'll be putting those arguments to the
Supreme Court and the Supreme Court will make its judgement."
The lead claimant in the case against the government, investment
fund manager Gina Miller, has said it is vital that the UK's
negotiating position is voted upon by MPs. She added that for this
not to happen would mean ministers were acting like a "tin-pot"
dictatorship.
There is some debate about whether a vote at Westminster on
invoking Article 50 would require a full Act of Parliament, or
whether it could happen much more speedily by MPs and peers
agreeing to a resolution - a written motion - instead.
But Brexit Secretary David Davis has suggested a full Act of
Parliament is more likely should the government lose its case.
In June's UK-wide referendum, voters opted by 51.9% to 48.1% in
favour of leaving the EU.