The House of Lords, which had wanted a series of changes to Prime Minister Boris Johnson's Brexit Withdrawal Bill, backed down at the final hurdle on Wednesday night, reported Xinhua news agency.
It came after lawmakers in the House of Commons used Johnson's 80-strong majority to reject the amendments demanded by the unelected upper change.
After a short debate in the House of Lords, peers bowed to the overwhelming support in the Commons and approved the Brexit bill.
There was no vote, with peers accepting the bill without any dissent.
It now means the Brexit bill will be presented to Queen Elizabeth II for Royal Assent.
The decision comes three and a half years after the people of Britain voted in June, 2016 by a 52-48 margin to leave the EU.
The passage of the bill was the final piece needed by Johnson to take Britain out of the EU at the end of this month.
Britain will continue to abide by Brussels' laws and procedures during 2020 to enable politic and officials from both sides to work out a permanent future relationship from January 1, 2021.
Johnson's bill contains a provision to prevent the temporary implementation period being extended beyond the end of this coming December.
Peers in the House of Lords lamented the fact that the House of Commons had refused to accept the changes they wanted.
The House of Commons rejected all five amendments put forward by peers in the unelected second chamber.
Brexit Secretary Stephen Barclay called on lawmakers in the Commons to reject the five amendments which covered issues such as child refugees and EU citizens living in Britain.
He described the bill as a piece of historic legislation.
( With inputs from IANS )