Labour leader Jeremy Corbyn suffered a major rebellion however, with nearly 50 of his own MPs defying his three-line-whip to back the bill and dozens more voting against a programme motion to extend debate on it.
But Labour leader Jeremy Corbyn faces a rebellion by some on his side, while the SNP and Liberal Democrats are also promising to oppose ministers.
Most MPs campaigned to stay in the European Union ahead of last June's referendum, but as debate on the bill began Tuesday, many said they would accept the result, however reluctantly.
May is expected to publish a "white paper", her detailed plan for Brexit on Thursday morning.
In the document, the government said: "We want to secure the status of European Union citizens who are already living in the United Kingdom, and that of United Kingdom nationals in other Member States, as early as we can".
The vote represents a victory for Prime Minister Theresa May, whose government aims to begin the two-year separation process officially at the end of next month.
Just in case you still feel short of information on Brexit, the government has confirmed that it will bring out a new white paper on the Great Repeal Bill, which transposes European Union regulation into British law.
It comes after MPs voted on Wednesday to allow May to begin the Brexit process.
Buried on page 32 of the Government's White Paper is the news that in Theresa May's post-Brexit nirvana all Brits will get a minimum of 14 weeks holiday a year, compared with four weeks under European Union laws.
Meanwhile, Britain's foreign secretary and prominent Leave campaigner, Boris Johnson, hailed the outcome of the vote.
Labour MP for Lancaster and Fleetwood, Cat Smith, had backed the Remain campaign in the June referendum, but voted in line with Mr Corbyn to support the Brexit bill.
Former deputy prime minister Nick Clegg told MPs he had heard "on very good authority" that Germany was ready to offer Mrs May an "emergency brake" on immigration in return for a form of Brexit which would minimise economic disruption.
She wrote: "I believe that Theresa May's Brexit "plan" is creating an unjustifiable level of risk at a time of national and worldwide uncertainty and volatility, with silence on national security measures, no mention of climate change mitigation or environmental protections, and no guarantee of good jobs or employment rights".
"The people of this country decided on June 23 previous year, with a slim but nevertheless clear majority, to leave the European Union".