Video report by ITV News Political Editor Robert Peston
The Government has won two key votes in the Lords - taking Britain a step closer to Brexit.
Prime Minister Theresa May can now begin formal talks on a divorce deal for leaving the EU.
Tonight, Brexit Secretary David Davis confirmed the Government would trigger Article 50 by the end of this month.
He said: "We are now on the threshold of the most important negotiation for our country in a generation.
"We have a plan to build a Global Britain, and take advantage of its new place in the world by forging new trading links.
"So we will trigger Article 50 by the end of this month as planned and deliver an outcome that works in the interests of the whole of the UK."
The House of Lords had made two amendments to the Bill.
Firstly introducing a "meaningful" vote on the final deal with Brussels.
This would have given the Lords and Commons the opportunity to accept or reject the final deal Mrs May negotiates with the EU prior to the UK's departure from the bloc.
The second amendment called to guarantee the rights of EU citizens living in the UK.
But both were rejected by MPs, and when the vote went back to the Lords, peers backed it unamended.
Brexit Secretary David Davis said the Government had a "moral responsibility" to the four million people EU nationals living in Britain.
But he dismissed concerns people would be deported if no deal is struck - and said Parliament would have to vote through any change to immigration rules.
He added: "I want to reassure people that Parliament will have a clear opportunity to debate and vote on this issue in future before anything else happens.
"So, nothing, nothing will change for any EU citizen in the UK without Parliament's explicit approval beforehand."
The Brexit Bill vote came on the same day as Nicola Sturgeon announced she would be seeking approval for a second referendum on Scottish independence.
The Scottish First Minister argued Scotland's interests had been ignored by Theresa May's administration ahead of Brexit negotiations.
Mrs May said Ms Sturgeon's decision was "deeply regrettable" and warned it would set Scotland on a course for "more uncertainty and division".
Responding to Ms Sturgeon's comments, Ms May said she would negotiate a Brexit deal which worked for "the whole of the UK - that includes the Scottish people".
If another referendum were to take place, it could be held as early as autumn 2018 - just four years on from when Scots voted by 55% to 45% to stay part of the United Kingdom.