MPs are due to spend two days debating the bill which was published last week, after the Supreme Court ruled parliamentary approval was needed before negotiations with Brussels could begin.
The two-clause European Union Notification of Withdrawal Bill asks parliament to give the prime minister the power to trigger Article 50 of the EU's Lisbon Treaty, formally starting divorce proceedings with Brussels.
Ahead of the debate Prime Minister Theresa May said lawmakers should back the Brexit bill in order to implement the June referendum outcome in which 52 percent voted to leave the bloc.
The governing Conservatives have a majority of 16 in the 650-seat lower House of Commons and the draft law is expected to pass, despite five amendments having been tabled.
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They cover areas including Britain's membership of the European single market, which May said would end once the country leaves the EU.
There are also calls to have greater involvement from the devolved parliaments of Wales, Scotland and Northern Ireland -- the latter two of which voted for Britain to remain in the EU.
Once it clears parliament the bill will move to the upper chamber, the House of Lords, where it will be debated from February 20 and it is expected to be approved there by March 7.
While further amendments could see the draft law bounce back to parliament for further discussion, politicians are unlikely to derail the government's Brexit plans.
If approved by the Lords, the bill would then have to be signed off by Queen Elizabeth II before May can trigger Article 50 which the prime minister has promised to do so by the end of March.
The timetable could be shorter still, however, as the EU's chief negotiator Michel Barnier said in December a deal should be brokered by October 2018 to allow for ratification on the EU side.