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.