Seven months after the historic referendum vote to leave the 28-nation bloc, the House of Commons is expected to grant its approval for May to trigger Article 50 of the EU's Lisbon Treaty.
The bill must now still pass through the House of Lords, where there may be more opposition from unelected peers less concerned about defying the majority of voters who backed Brexit.
But if, as expected, the bill passes its Commons stage in a vote late Wednesday, May will be significantly closer to her goal of starting the two-year exit talks by the end of March.
Under pressure from MPs, the government was forced to concede on Tuesday that parliament would have a vote on the final Brexit deal before it is signed off.
The move helped fend off a rebellion by pro-European members of May's Conservative party, who had threatened to back an opposition amendment to the two-clause bill.
But ministers stressed that if lawmakers rejected the final deal, the alternative was not to return to negotiations but to leave the EU without an agreement.
"This will be a meaningful vote. It will be a choice between leaving the European Union with a negotiated deal or not," Brexit minister David Jones said.
'Nightmare scenario'
More than two-thirds of MPs campaigned against Brexit in the June referendum, but after 52 percent of Britons voted to leave the EU, most have reluctantly accepted that they must uphold the result.
When May introduced her Brexit bill last month, following a Supreme Court ruling that she must seek parliament's approval to start the process, the opposition Labour party promised not to block it.
Some 47 Labour MPs rebelled to vote against the legislation, backed by the Scottish National Party (SNP) and the smaller Liberal Democrats party, and more could defy their party leadership on Wednesday.
In a symbolic move on Tuesday, the SNP-dominated Scottish Parliament voted overwhelmingly against the bill passing through Westminster.
But there are not enough critics to thwart the bill, and efforts to amend it to tie the government's hands in negotiations have so far failed.
Many MPs are opposed to May's decision to prioritising controlling EU migration into Britain in the talks, at the cost of losing membership of Europe's single market.
Brexit minister Jones said the "final draft agreement" on leaving the EU would be put to MPs and peers before it was put to the European Parliament for ratification.
A number of lawmakers are sceptical that both the exit terms and a new trade deal can be agreed within two years of talks.
But Jones said he was confident of getting agreement on both areas, but said that if there was no deal, Britain would fall back on World Trade Organization rules to determine its trade with the EU.
Labour MP Chris Leslie warned: "On the nightmare scenario, that we could leave the EU with no deal at all, and face damaging barriers to trade with Europe, it seems parliament could have no say whatsoever."
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