"To reduce pressures on local communities, we will also house people on ships," PM Sunak told a news conference.
"The first will arrive in Portland next week and we've secured another two today that will accommodate another 1,000."
Meanwhile, on a visit to the Channel port of Dover, Sunak announced new sites at former Royal Air Force bases to accommodate "hundreds" in the coming months.
Sunak, who visited the operations room tracking small boat crossings, claimed the asylum system was being "overwhelmed" by exploitative criminal gangs.
"Nearly 3,000" will be housed there by the end of the year, he added, arguing it would ease pressure on costly hotels where many migrants have been staying.
Sunak, pushing proposed new laws currently in parliament to criminalize asylum-seekers arriving via the Channel, claimed the crackdown was working.
A total of 7,610 people have been detected in small boats so far this year, according to government figures.
"Crossings are down 20 percent compared to last year," Sunak said, adding: "Illegal migrants entering the rest of Europe have risen by 30 percent."
Supporters of the U.K.'s bid to leave the European Union made "taking back control" of the country's borders a key plank of their Brexit campaign.
With the U.K. now out of the E.U., immigration remains a live political issue, particularly as a general election approaches next year.
Last month, Sunak said legal immigration levels were also "too high" and announced restrictions on family visas for international students.
Asylum applications, however, are still well below those in European countries such as France and Germany.
Just over 33,000 people were waiting more than six months for an initial decision on asylum by the end of December 2021, out of a total of 82,000 applications.
By the same time last year, that figure had ballooned to nearly 89,000 out of just over 132,000 applications, according to the Oxford Migration Observatory.
But Sunak said the backlog had now been cut by over 17,000.
With the U.K. no longer part of the E.U.'s migrants policy, the government has been forging returns programs with individual countries on mainland Europe.
A new multi-million-euro partnership with France has also been signed to prevent small boats crossings in the first place.
But a controversial deal to deport failed asylum-seekers to Rwanda, denounced by human rights groups, is stuck in the courts.
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