Brexit Secretary David Davis said the Government had a "moral responsibility" to the four million people this affected.
The legislation then went back to the House of Lords, where Labour abstained in order to avoid being seen as attempting to overrule the will of democratically-elected MPs.
Once the bill gets the so-called royal assent on Tuesday and becomes law, it will be up to Theresa May to fire the starting pistol and invoke Article 50 of the Lisbon Treaty, the exit procedure from the EU.
May will officially have the authority to trigger Article 50.
The Conservative premier also attacked First Minister of Scotland Nicola Sturgeon, who on Monday called for a second Scottish independence referendum.
The House of Commons will debate and vote on Monday on the Brexit bill that was passed by the House of Lords last week with two amendments - the key issue is whether MPs will uphold the amendments or overturn them.
"Parliament has today backed the government in its determination to get on with the job of leaing the European Union and negotiating a positive new partnership with its remaining member states", Davis said.
Prior to the vote in parliament, a report from Migration Watch UK had called for the introduction of a temporary two-year work permit for EU Nationals in the UK post-Brexit to help employers to plan ahead.
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Theresa May has told MPs that the backing for the government's Brexit bill will be a "defining moment for our whole country".
But he also warned that the European Parliament will have veto powers and could reject any deal brokered between the United Kingdom and the European Commission. In an earlier referendum in 2014, Scotts had voted to remain part of the UK.
"You can't have a hard Brexit and a successful economy", he said.
Labour's Jeremy Corbyn accused the government of being "complacent".
The UK has taken one step closer to leaving the European Union on March 13 as Parliament approved a bill to launch the Brexit procedure in its original form, without amendments.
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".
Prime Minister Theresa May has said she is optimistic about settling the divorce and a new trade agreement with the European Union within the timeframe, but would walk away rather than accept a bad deal.
That could make Prime Minister Theresa May's two-year timetable significantly more hard, with migration and agriculture expected to be particularly divisive topics within the Conservative party.
However, the government never had any intention of triggering Article 50 before the last week of March, a Number 10 spokeswoman said Monday.