Boris Johnson is set to unveil the plans later, before Home Secretary Priti Patel signs a migration deal with the African nation.
The trial scheme would mean single men arriving in Britain via Channel crossings could be forcibly removed.
Refugee organisations have criticised the plans as cruel and urged a rethink.
Labour said the plan was "unworkable, unethical and extortionate" - and one designed to "distract" from Mr Johnson's fine for breaking Covid-19 laws.
The Liberal Democrats said the proposal would be "expensive for taxpayers, while doing nothing to stop dangerous Channel crossings or combat the smuggling and trafficking gangs".
The deal is expected to see the Rwanda, which is part of the Commonwealth, given an initial £120m as part of a trial, but opponents say the annual cost of the full scheme would be far higher.
In a speech in Kent, Mr Johnson will argue that action is needed to stop "vile people smugglers" turning the ocean into a "watery graveyard".
Last year, 28,526 people are known to have crossed the English Channel in small boats, up from 8,404 in 2020.
Around 600 people made the crossing on Wednesday, and Mr Johnson will say the figure could reach 1,000 a day within weeks.
"We cannot sustain a parallel illegal system," he will say. "Our compassion may be infinite, but our capacity to help people is not."
The prime minister will announce plans to hand operational control of the Channel to the navy, break the business model of people-smuggling gangs, and deter people from risking the crossing.
The measures are part of the government's long-term plan to "take back control of illegal immigration" after Brexit, Mr Johnson will say.
While the number of people crossing the Channel in boats has increased, last year saw fewer people using other routes - such as by lorry - in part because of increased security at the Port of Calais.
The UK/Rwanda Migration and Development Partnership is the centrepiece of a wider policy blitz to deal with what has been a humiliation for ministers who promised Brexit would mean control of Britain's borders.
Instead, record numbers of asylum seekers have been turning up in dinghies beneath the white cliffs of Dover. This year has already seen 4,578 arrivals and looks set to be a new record.
Sending asylum seekers to Rwanda, however, is likely to prove hugely controversial and legally fraught.
Critics point to Rwanda's poor human rights record. At the UN last year, the UK demanded investigations into alleged killings, disappearances and torture.
Ministers will have to explain why Rwanda is the right place to entrust with protecting the human rights of vulnerable asylum seekers who hoped the UK would protect them.