Prime Minister Theresa May will return to the Commons later in month to inform MPs when she has triggered Article 50 of the Lisbon Treaty.
If the bill passes Monday, May could announce she is triggering Article 50 as early as Tuesday.
The European Parliament's chief Brexit negotiator has warned against trying to sideline the assembly once talks over the UK's exit from the EU begin.
The upper chamber backed a Labour-led change calling for ministers to take action to ensure the rights of European Union nationals continue within three months of Article 50 being triggered.
Peers then voted 274 to 118, Government majority 156, against a move to insist on a "meaningful" vote on the final deal.
The referendum also brought the resignation of former Prime Minister David Cameron, who during a re-election campaign had promised to hold the vote.
Ahead of the French vote, there will be a reluctance to imply that the United Kingdom can get a good deal from leaving the European Union as this would risk increasing support for populist parties.
The committee, which previously criticized the government's failure to plan for Britons voting to leave the European Union at last year's referendum, said making such preparations would also add credibility to the government's position that it is prepared to walk away from a bad deal.
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Numerous firefighters battling the blaze had just come from the funeral of a retired firefighter who died of cancer, he said. Dennis DeVoe was heading to the scene when his vehicle was hit in an intersection.
"As we embark upon the most complex set of negotiations our country has ever faced, it would have been greatly preferable to have guaranteed a meaningful vote for MPs at the end of the process".
There is speculation that May could wait to trigger Article 50 until after a Mar 25 summit in Rome to mark the EU's 60th birthday, a moment it hopes will emphasise the bloc's unity.
With all the legal hurdles out of the way, PM May is free to trigger Article 50.
Both houses backed the "Brexit bill" and after securing symbolic approval from Queen Elizabeth, expected in the coming days, May has the right to begin what could be Britain's most complex negotiations since World War ll. The evidence clearly shows that a majority of people in Scotland do not want a second independence referendum.
First Minister Nicola Sturgeon said her concerns about May's plan to pull Britain out of Europe's single market, in order to cut immigration, had been met with a "brick wall of intransigence".
The EU may be seen to have the upper hand in the negotiations.
The parliament in the United Kingdom voted against landmark legislation passed by the House of Lords to protect the status of European Union nations within three months of the start of Brexit talks.
Speaking on ITV's Peston on Sunday he said: "I think we've got every prospect of doing a very good deal between now and the end of the negotiating period in 2019". "Every member state has reinforced the point - they want this at the top of the agenda, they want this to be dealt with first", he said, promising a quick deal.