The home secretary says a new treaty with Rwanda addresses the concerns of the UK's Supreme Court, which ruled the government's plan unlawful last month.
The court said the policy, which would see migrants sent to Rwanda, was open to human rights breaches.
James Cleverly insisted Rwanda had made "a clear and unambiguous commitment to the safety of people who come here".
The policy is part of the government's plan to deter migrants from crossing the Channel in small boats.
Prime Minister Rishi Sunak has said "stopping the boats" is one of five main priorities for his government ahead of the next general election.
But the Rwanda scheme - which was first announced by former Prime Minister Boris Johnson in April 2022 - has been repeatedly delayed by legal challenges and no asylum seekers have been sent to the country yet.
Labour has also pledged to scrap the policy if it wins the next election, casting doubt over its long-term future.
Shadow home secretary Yvette Cooper said the policy was "failing" - and funding for it would be better spent on "going after" the gangs that organise small boat crossings.
The Supreme Court, the UK's highest court, rejected the policy on the grounds that it could not be guaranteed the Rwandan government would honour a principle of international law known as non-refoulement.
The principle forbids a country that receives asylum seekers from returning them to any country if doing so would put them at risk of harm.
Following the ruling, Mr Sunak said his government would work on a new treaty with Rwanda and said he would introduce emergency legislation to assert the country was safe.
The legislation is expected to be introduced in Parliament this week.
Court concerns
Mr Cleverly travelled to Kigali and signed the new legally binding treaty alongside Rwanda's foreign affairs minister Vincent Biruta on Tuesday.
He is the third home secretary to make his way to Rwanda - following in the steps of his predecessors Priti Patel and Suella Braverman.
The British government says the new treaty ensures that people relocated to Rwanda are not at risk of being returned to a country where their life or freedom would be threatened.
The treaty establishes a new appeal body, which will be made up of judges with asylum expertise from a range of countries, to hear individual cases.
The government says Rwanda's asylum system would be monitored by an independent committee, whose powers to enforce the treaty would be beefed up.
The Monitoring Committee will develop a system which will enable relocated people and their lawyers to lodge complaints, the government says.
At a press conference, Mr Cleverly insisted Rwanda was a safe country and said "we feel very strongly this treaty addresses all of the issues of their lordships in the Supreme Court".
He said this would be "reflected in domestic legislation soon".
A spokesperson for the Rwanda's government said it had a "proven record" of offering a home to refugees, and the new treaty would "re-emphasise, in a binding manner, already existing commitments" on asylum seeker protection.
The asylum policy has already cost the UK government at least £140m, but Mr Cleverly said the UK has not paid Rwanda any additional money for the new treaty.
The home secretary said he could not see "any credible reason" to question Rwanda's "track record" of handling asylum cases and he hoped to see the scheme running "as quickly as possible".
He said Rwanda had a "strong reputation" of being humane and was "uncomfortable" at the "tone" of the criticism levelled at Rwanda.
Rwanda's foreign affairs minister suggested "internal UK politics" may have played a role in the asylum policy being blocked.
But Mr Biruta said: "I would say there's always room for improvement to any system designed by human beings, Rwandan or British.
"This is the reason why we have worked on this treaty... to make sure we can improve our asylum system and that we have a fair and transparent asylum system in place."
Tory disquiet
Conservative MPs on the right of their party are putting pressure on Mr Sunak to stop migrant boat crossings.
More than 45,700 people crossed the Channel to come to the UK in 2022, the highest figure since records began.
In the coming days, the government will bring forward new legislation to try to avoid more legal challenges to its Rwanda plan.
The One Nation Caucus of Conservative MPs have expressed concerns about the legislation and fear it may seek to ignore UK and international human rights laws.
Some Tory MPs argue that withdrawing the UK from the European Convention on Human Rights (ECHR), an international treaty, would stop the Rwanda scheme from being blocked by legal challenges.
But senior Tory MP Damian Green said Conservatives like him "hold these treaties dear and they should be seen as fundamental to part of protecting the UK's democratic legacy".
The UK government is also facing calls to slash net migration, which has soared to a record 745,000 in 2022.
The Conservatives have repeatedly promised to cut net migration since winning power in 2010, and "take back control" of the UK's borders following the Brexit vote.
On Monday, the home secretary announced a package of measures including raising the minimum salary needed for skilled overseas workers from £26,200 to £38,700.
Mr Cleverly claimed 300,000 people who were eligible to come to the UK last year would not be able to in future.
