The Government’s Rwanda deportation plan passed through Parliament following an extended tussle between MPs and Lords.
The unelected chamber ended the deadlock after MPs rejected a requirement that Rwanda could not be treated as safe until the secretary of state, having consulted an independent monitoring body, made a statement to Parliament to that effect.
The Government said the Lords amendment was "almost identical" to the previous ones overturned by MPs.
Having completed its parliamentary passage, the Bill now goes for royal assent.
Rishi Sunak said the bill was 'a fundamental change in the global equation on migration.'
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In a statement, Rishi Sunak said: "The passing of this landmark legislation is not just a step forward but a fundamental change in the global equation on migration. We introduced the Rwanda Bill to deter vulnerable migrants from making perilous crossings and break the business model of the criminal gangs who exploit them.
"The passing of this legislation will allow us to do that and make it very clear that if you come here illegally, you will not be able to stay. Our focus is to now get flights off the ground, and I am clear that nothing will stand in our way of doing that and saving lives."
Home secretary James Cleverly said: "The Act will prevent people from abusing the law by using false human rights claims to block removals. And it makes clear that the UK Parliament is sovereign, giving Government the power to reject interim blocking measures imposed by European courts.
"I promised to do what was necessary to clear the path for the first flight. That’s what we have done. Now we’re working day in and day out to get flights off the ground."
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Home Secretary James Cleverly and Defence Secretary Grant Shapps
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Meanwhile, shadow home secretary Yvette Cooper called the Bill "an extortionately expensive gimmick rather than a serious plan to tackle dangerous boat crossings."
The MP for Normanton, Pontefract and Castleford said: "The Rwanda scheme will cost more than £500,000,000 for just 300 people, less than one per cent of asylum seekers here in the UK – and there is no plan for the 99 per cent.
"Instead of spending £2million per asylum seeker on this failing scheme they should be putting that money into boosting our border security instead, that is Labour’s practical plan. This is the third new law the Tories have passed on Channel crossings in two years, each one has made the chaos worse and even senior Tory MPs don’t believe this third law will work.
"As former immigration minister Robert Jenrick has said this is just a plan to get a few symbolic flights off before an election. Now the new law has passed, the Conservatives will immediately sign another £50m cheque to Rwanda on top of the £200m sent so far, even though not a single asylum seeker has yet been sent."
Shadow home secretary Yvette Cooper
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Earlier in the day, Rishi Sunak blamed Labour peers for holding up the Bill, as he acknowledged he will miss his self-imposed spring target for getting the Rwanda scheme off the ground.
A government source told The Telegraph: "As soon as the treaty is ratified and we have got Royal Assent, we will start getting people ready – and that includes detention."
Chief executive of the Refugee Council Enver Solomon said: "Even if, as the Prime Minister asserts, there is to be ‘a regular rhythm of multiple flights every month’, this will still only correspond to at most a few thousand people a year out of tens of thousands.
"Instead of giving these people a fair hearing on UK soil to determine if they have a protection need, the Government will have to look after them indefinitely at considerable cost."