Supreme Court judges unanimously rejected claims that Scotland, Wales and Northern Ireland should be given a veto on Brexit.
Scotland's First Minister Nicola Sturgeon led arguments that the devolved administrations should be consulted before Theresa May triggers Article 50 - the formal mechanism for leaving the European Union - which threatened to derail the PM's timetable for Brexit.
The case came alongside the main Supreme Court ruling that MPs must be consulted before the government starts the process of leaving the EU.
The Scottish Nationalist Party said it will put forward 50 ''serious and substantive'' amendments to the legislation.
Former first minister Alex Salmond, the SNP's international affairs spokesman, said, ''We welcome the Supreme Court's decision and hope that their ruling brings this Tory government back to the reality that they cannot simply bypass elected parliamentarians to fulfil their role in carrying out due and proper scrutiny of one of the biggest decisions facing the UK.
''The Prime Minister and her hard Brexit brigade must treat devolved administrations as equal partners - as indeed she promised to do.
''For over six months the concerns surrounding a hard Tory Brexit have been echoing throughout the land and yet the prime minister has not listened.
''If Theresa May is intent on being true to her word that Scotland and the other devolved administrations are equal partners in this process, then now is the time to show it. Now is the time to sit with the Joint Ministerial Committee and not just casually acknowledge, but constructively engage. Consultation must mean consultation.''
Explaining why they decided the Scottish Parliament and Welsh and Northern Ireland Assemblies do not have to be consulted before triggering Article 50, the Supreme Court judges said, ''The devolution Acts were passed by parliament on the assumption that the UK would be a member of the EU, but they do not require the UK to remain a member.
''Relations with the EU and other foreign affairs matters are reserved to UK government and parliament, not to the devolved institutions. Withdrawal from the EU will alter the competence of the devolved institutions, and remove the responsibilities to comply with EU law.
''In view of the decision of the majority of the Justices that primary legislation is required for the UK to withdraw from the EU, it is not necessary for the court to decide if the NIA imposes a discrete requirement for such legislation
''The decision to withdraw from the EU is not a function carried out by the Secretary of State for Northern Ireland in relation to Northern Ireland within the meaning of section 75 NIA.''
They added, ''Moreover, section 1 NIA, which gave the people of Northern Ireland the right to determine whether to remain part of the UK or to become part of a united Ireland, does not regulate any other change in the constitutional status of Northern Ireland.
''As to the application of the Sewel Convention to the decision to withdraw from the EU given the effect on the devolved competences, the Convention operates as a political constraint on the activity of the UK Parliament. It therefore plays an important role in the operation of the UK constitution.
''But the policing of its scope and operation is not within the constitutional remit of the courts. The devolved legislatures do not have a veto on the UK's decision to withdraw from the EU.''