The Brexit bill has been approved by Parliament, allowing Theresa May to trigger Article 50 and begin the process of leaving the European Union.
With no opposition from Labour, the House of Lords backed down in their attempts to amend the bill following an earlier vote in the Commons.
MPs rejected a Lords amendment to guarantee the status of EU nationals resident in the UK by a margin of 335 votes to 287.
They also overturned a second amendment, which would have required the Government to grant Parliament a "meaningful" vote on the Brexit deal eventually secured by Mrs May, by 331 votes to 286.
Speaking after the vote the Brexit Secretary David Davis said: "Parliament has today backed the Government in its determination to get on with the job of leaving the EU and negotiating a positive new partnership with its remaining member states.
"We are now on the threshold of the most important negotiation for our country in a generation."
Labour leader Jeremy Corbyn responded saying it was "deeply disappointing" the Government had refused to give ground but it was "only the start of the process".
"Labour, at every stage, will challenge the Government's plans for a bargain basement Brexit with Labour's alternative of a Brexit that puts jobs, living standards and rights first," he said.
Theresa May looks set to wait until the end of the month before kicking off the two-year process of negotiating departure from the EU.
There was speculation that the Prime Minister would move immediately to start Brexit in a statement to the Commons on Tuesday, after gaining the legal authority.
But her official spokesman poured cold water over the rumours, telling reporters that the PM had always said she would trigger Article 50 by the end of March.
He added: "I've said 'end' many times but it would seem I didn't put it in capital letters strongly enough."
Wednesday and Thursday this week are viewed as politically sensitive as it would coincide with elections in the Netherlands, where the anti-EU PVV party of Geert Wilders is challenging for a share in power.
Triggering Article 50 next week could be seen to overshadow the special summit of the remaining 27 member states in Rome on 25 March to mark the 60th anniversary of the European Union.
The PM's European counterparts had been prepared for her to make an announcement this week, with 6 April pencilled in as the date for a meeting of the 27 other EU leaders to respond to the situation - a gathering which will now be pushed back until later that month.
Amid occasionally angry scenes, peers took just two hours to decide not to defy the will of the elected Commons.
Conservative ex-Cabinet minister Viscount Hailsham, who had previously backed the "meaningful" vote amendment, said: "We have asked the Commons to think again, they have thought again, they have not taken our advice, and our role now I believe is not to insist."
Independent crossbench peer Lord Pannick, who represented Gina Miller in her Supreme Court action to force the Government to give Parliament a vote ahead of Article 50, said it was time for the Lords to "give way on this matter".
Some Liberal Democrats continued with attempts to stop the bill going through unopposed.
Lib Dem Lord Taverne said: "It is a very dangerous step towards the doctrine that the people's will must always prevail.
"This is the doctrine which has always been favoured by Hitler, by Mussolini, by Stalin, by (Turkish president) Erdogan at this present time.
"It is denial of the essence of democracy which we have supported to great effect in this country, and now we are abandoning it."
Analysis showed that 25 Labour peers sided with the Lib Dems, including former Cabinet minister Lord Mandelson.