Lawmakers voted by 326 to 290 in favour of backing the legislation, after more than 13 hours of debate, which will now go forward for further scrutiny by MPs.
The bill is aimed at repealing the 1972 law through which Britain joined the bloc, transferring in bulk around 12,000 existing EU regulations onto the British statute books.
It is the next step in implementing last year's historic referendum vote to leave the EU, after Prime Minister Theresa May formally notified Brussels of Britain's withdrawal in March.
May's Conservative government won Tuesday's parliamentary vote thanks to its alliance with the Northern Ireland's Democratic Unionist Party (DUP).
The premier described the outcome as a "historic decision" which "gives certainty and clarity ahead of our withdrawal from the European Union".
"Although there is more to do, this decision means we can move on with negotiations with solid foundations and we continue to encourage MPs from all parts of the UK to work together in support of this vital piece of legislation," May said in a statement.
The main opposition Labour party had voiced its objection to the bill, arguing that its provisions to smooth the transfer of EU laws represent an unacceptable expansion of executive power.
Many EU regulations may need adjusting as they are transferred, and the bill proposes the broad use of existing "Henry VIII powers" that allow ministers to amend legislation without full parliamentary scrutiny.
Labour lawmaker Chris Bryant said such powers would lead to "a dangerous spiral of autocracy".
"It pretends to bring back power to this country, but it actually represents the biggest peace time power grab by the executive over the legislature, by the government over parliament, in 100 years," he told parliament.
A total of seven Labour MPs however rebelled against the party line and backed the bill.
Brexit deal uncertainties
While most MPs have accepted that Brexit will happen, the shape of the European divorce remains unclear and May has been under pressure from all sides after losing her parliamentary majority in the June snap election.
The government plans to leave Europe's single market and customs union after Brexit but is seeking a transitional deal that would replicate existing arrangements until it agrees a new trade deal with the EU.
Labour wants to remain in the single market during the interim period following Brexit day, currently set for March 29, 2019, while a eurosceptic group of Conservatives is pressing May to make a clean break.
Such issues will need to be agreed with the EU, and the Repeal Bill does not propose any changes in policy.
But it does give ministers the power to implement the final Brexit deal without full parliamentary debate.
"It would be ministers who decided our new trade arrangements, customs arrangements and immigration rules, any deal on citizens' rights and much else," Labour Brexit spokesman Keir Starmer wrote in the Sunday Times newspaper.
Labour and trade unions also fear ministers may seek to change EU regulations on the environment and workers' rights as they transfer them into UK law.
"We are seriously concerned that the power-grab embodied in the bill will end up with worker's rights being watered down," Frances O'Grady, head of the Trades Union Congress umbrella body, told AFP.
Brexit Secretary David Davis denies this, saying the bill is a "pragmatic and sensible" way to deal with the huge amount of EU legislation that must be incorporated into British law.
"Without it, we would be approaching a cliff-edge of uncertainty which is not in the interest of anyone," he said.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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