The Government won with a majority of 99.
The bill will now go to the House of Lords; any amendments passed by peers will see it return to the House of Commons.
The prime minister's official spokesman warned the House of Lords, where Johnson does not have a majority, not to frustrate the progress of the legislation. It is expected to become law before the 31st of January.
Winding up the debate on the bill, Brexit Secretary Steve Barclay said: "This evening the bill will pass to the other place with a very clear mandate from this House that now is the time to move forwards".
Brexit Party leader Nigel Farage has told Prime Minister Boris Johnson to get tough in trade deal negotiations with Brussels.
"It is my honest hope that their lordships will now give due regard to the clear majorities we have seen during the committee stage and establish their endorsement of this bill in a similar, timely, fashion", Brexit Secretary Steve Barclay told lawmakers.
Speaking of his former role leading the national work across local government on the resettlement of refugees in the UK, Mr Simmonds (Ruislip, Northwood and Pinner) said: "What tends to happen is young people are brought to Britain to be linked up with a distant cousin and in fact, they nearly immediately become an accompanied asylum-seeking child and therefore in the care system of this country".
Tory David Simmonds said, while it is clear that issues around the resettlement of vulnerable children are "very much in the minds of many members", it is "absolutely right" that these issues are for the Immigration Bill, rather than the Withdrawal Agreement Bill (Wab).
London did not want the EU's long-standing policy that "nothing is agreed until everything is agreed" - meant to stop one side cherry-picking bits of a deal they like - to define the coming negotiations, a spokesman said.
"If the United Kingdom wants an open link with us for the products - zero tariffs, zero quotas - we need to be careful about zero dumping at the same time", he told a conference in Stockholm.
'"I hope that this point is, and will be correctly understood by everybody".
"We will ask necessarily certain conditions on state aid policy in the UK", Barnier said.
Sources said that during the private talks, Mr Johnson was to tell the Commission president that "having waited for over three years to get Brexit done, both British and European Union citizens rightly expect negotiations on an ambitious free trade agreement to conclude on time" and that "the upcoming negotiations will be based on an ambitious FTA [free trade agreement], not on alignment".
Barnier, speaking in Sweden, added the European Union "will strive for partnership that goes well beyond trade ... but that is a very huge agenda, and we simply can not expect to agree on every single aspect of this new partnership" in less than a year.