The case was considered the most important constitutional issue in a generation, clarifying who ultimately wields power in Britain's system of government: the prime minister and her Cabinet, or Parliament.
The House of Commons and the House of Lords will debate the bill and then vote on it.
British Prime Minister Theresa May said Wednesday she would publish her Brexit plan in parliament so that MPs can scrutinise it, but insisted the government's timetable was on track.
In essence, the government argued that even though triggering Article 50 would lead to a change in domestic law and fundamentally alter the constitutional arrangements that European Union membership had wrought, it should be allowed to trigger it without parliamentary consent.
Responding to Tuesday's ruling, 10 Downing Street noted that Parliament had previously backed the idea of Brexit, when it approved the plan to hold a referendum. The Supreme Court also found May did not need permission from the devolved administrations-Wales, Northern Ireland and Scotland-to trigger Article 50.
A Whitehall source said Brexit Secretary David Davis was meeting Mayor Sadiq Khan regularly and was "very alive to the concerns of the capital". While it is unlikely MPs will vote against invoking Article 50, they could delay the process and seek concessions from the government. And Liberal Democrat chief Tim Farron said his members of Parliament would vote against the bill unless the public as a whole could vote anew on a final deal.
It is hard to imagine such efforts succeeding, but this does not mean the process in the House of Commons will be a comfortable one for the government.
Scottish Conservative leader Ruth Davidson accused the SNP of using the Supreme Court case "to hold the United Kingdom to ransom". He added that any MP who voted against triggering Article 50 would be attempting to effectively "thwart the will of the people".
May's government tried to stop the vote via its appeal, on which the country's supreme court had to rule.More news: Sandy Kenyon reviews 'Split,' directed by M. Night Shyamalan
The Government is refusing to reveal how much money has been spent on lawyers to fight Theresa May's two failed Brexit legal challenges.
The government alone can not interpret what the referendum result means and where we go from here - they have to bring forward legislation that will be scrutinised and debated by parliament.
The government did have one clear win in the ruling. "We should all welcome it".
Holyrood will bid to block Brexit despite Supreme Court judges ruling it does not have the legal powers to do so, Nicola Sturgeon has said.
In an eight-to-three decision, the Supreme Court said Parliament must vote on government's move to invoke Article 50 of the Lisbon Treaty, which is the exit mechanism.
The court ruled Theresa May can not trigger Article 50 - the formal exit process from the European Union - without the backing of MPs and peers.
"We are not being asked to overturn the result of the European Union referendum", David Neuberger, President of the Supreme Court said at the conclusion of a four-day hearing.
"The 2016 referendum is of great political significance".
"The UK constitution requires such changes to be effected by Parliamentary legislation", it concluded.