The legislation, which passed despite government opposition to it, will now return to the elected House of Commons for further consideration, with a view to being finalized and becoming law later on Monday, according to Reuters.
Parliament seized control of the Brexit process from May last month and is expected to agree a last-ditch deal on the terms of exit before an EU emergency summit on Wednesday.
The UK and the EU reached a divorce deal late last year, but the UK Parliament has refused to back the agreement and cannot agree on any alternative measures. The country was supposed to have left the bloc on 29 March but missed the deadline. The European Union gave London until 12 April to either come up with an alternative solution or leave without a deal on that day.
Brussels said last week it was not convinced by May's request to put off the United Kingdom’s departure until 30 June. European Commission President Jean-Claude Juncker warned 12 April was the ultimate date for London to approve the Brexit deal.