The House of Commons supported it despite opposition from the SNP, Liberal Democrats and some Labour rebels
MPs have backed the bill to allow the Prime Minister to trigger Article 50 - the start of the formal process of leaving the EU.
In what was politicians' first chance to vote on the Brexit legislation, the House of Commons supported it despite opposition from the SNP, Liberal Democrats and some Labour rebels.
It passed by 498 votes to 114, a majority of 384.
A SNP amendment to halt the bill because it was argued there was not enough consultation was earlier defeated by 336 votes to 100.
Now the bill has overcome its opening test, it will continue its path through Parliament over coming weeks, including at committee stage.
Theresa May is due to trigger Article 50 by the end of March and then the Prime Minister will begin official Brexit negotiations with EU officials.
Labour leader Jeremy Corbyn had ordered his MPs to back the bill but less than an hour before voting, two members of the shadow cabinet, Dawn Butler and Rachael Maskell, resigned so they could defy him.
On Thursday, the Government will publish its white paper setting out its strategy for EU withdrawal.
The two-day debate in Westminster saw passionate speeches from both sides of the argument, with veteran Eurosceptics hailing the historic vote and Brexit opponents explaining their decisions to either oppose or support the bill.
Former Chancellor George Osborne, who was accused of masterminding 'Project Fear' by Vote Leave, said he was saddened that Britain was now "bracketed in the same group as other isolationist and nativist movements around the world."
Justifying his support for the bill, he said: "I lost the case. I made it with passion, I sacrificed my position in Government for it and in the end we have to now accept that in a democracy the majority has spoken."
"Whilst I am a passionate believer in an open, internationalist, free-trading Britain, I'm also a passionate believer in Britain as a democracy," he added.
But his role in the Remain campaign was criticised by the SNP's Alex Salmond who went on to accuse fellow MPs of being "gripped by collective madness".
"The right honourable member for Rushcliffe (Kenneth Clarke) yesterday compared it to Alice in Wonderland," he said.
"But Alice only took herself into the hole. This Prime Minister is taking virtually all of the Tory Party, half the Labour Party and the entire country into the hole."
"It is politically crazy, what is being done," he added.
The Liberal Democrat leader Tim Farron, who had been ridiculed by MPs for claiming to be the official Brexit opposition but had missed much of Tuesday's debate, warned against a "government stitch-up".
Calling for another vote on the final divorce settlement he said: "Both the Labour front bench and the Conservatives don't want to give the British people their say; they think they know better."
"It is an arrogance. It is anti-democratic," he argued.
Throughout the afternoon a number of Labour MPs told the House they were prepared to defy the party whip, including Hampstead and Kilburn MP Tulip Siddiq, Chris Bryant and Stella Creasy.
Labour MP Neil Coyle traduced his own leader for supporting the bill and was told by the Speaker to apologise after saying the country was run by "a whole Government full of b*******".
And in her maiden speech Dr Caroline Johnson, who won last month's by-election in Sleaford and North Hykeham, announced she would be supporting the bill to trigger Article 50.
"I was brought up to believe that a good democracy is ruled by the majority with protection for minorities," she said
"As I talked to my constituents I increasingly understand that they perceive we are ruled by a vocal, minority elite, who are disregarding the views of the majority - and they're angry."
Arguably the most inventive speech came from the SNP's Hannah Bardell, who said she was inspired after watching Trainspotting 2.
"Choose Brexit. Choose making up numbers and plastering them against buses. Choose racist sentiment. Choose race crime rising. Choose taking the people of our nations to the polls with nothing written down and no plan."
She concluded: "These are not the choices Scottish people made."