The judgement means the British Prime Minister cannot trigger Article 50 of the Lisbon Treaty to officially begin Brexit negotiations with the 28-member EU until Britain's MPs and peers give their backing.
It has now confirmed that a new bill will be tabled in Parliament "within days" for this purpose.
The government had argued that it already had the executive powers to trigger Article 50but Supreme Court judges rejected the case by a majority of eight to three.
The official judgement in the case concludes: "The change in the law required to implement the referendum's outcome must be made in the only way permitted by the UK constitution, namely by legislation.
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"In a joint judgement of the majority, the Supreme Court holds that an Act of Parliament is required to authorise ministers to give notice of the decision of the UK to withdraw from the European Union."
Reacting to the verdict, UK Secretary of State for Exiting the European Union David Davis told the House of Commons, "The judgement does not change the fact the UK is leaving the EU...A Bill will be introduced within days. It will be as straightforward as possible...The government will respect the Supreme Court decision. And Parliament must respect the views of the people expressed in the referendum."
Downing Street had been preparing for the result for weeks and revealed that it had drafted a "straightforward" bill to seek parliamentary approval to trigger Article 50.
Davis stressed that he hoped that MPs will try not to "frustrate the process".
The court hearing alsoincluded arguments from Scotland, Wales and Northern Ireland as interested parties in the case.
The Supreme Court, however, ruled that the devolved Scottish Parliament and Welsh and Northern Ireland assemblies did not need a say in the formal Brexit process.