Boris Johnson has instructed government departments to devise a new fast-track visa system to attract leading scientists to work in the UK.
The PM plans to scrap the cap on "tier one" visas for highly skilled migrants - currently the limit is 2,000 a year.
He also wants to make the system easier for scientists and their families.
Science bodies have welcomed the proposals but warn any benefits to research would be greatly outweighed by the damage caused by a no-deal Brexit.
The prime minister made the announcement at the Culham science centre in Oxfordshire which undertakes research on fusion power.
The Home Office and the Department for Business, Energy & Industrial Strategy (Beis) are the departments involved in preparing the new visa process.
Speaking exclusively to BBC News about the announcement, he said that he wanted to see a greater openness to scientific top talent from around the world.
"We're going to turn the UK into a kind of supercharged magnet, drawing scientists like iron filings from around the world coming to help push forward projects like this (fusion research in Culham) in which we can not only take a scientific lead but a commercial lead as well," he said.
EU researchers account for half of the total UK scientific workforce of 211,000. Currently, they don't need visas to work in British labs.
Those from outside the UK currently need to go through a rigorous process supervised by the Home Office. The process is time consuming, taking up to 100 days and costly, with a bill of about £8,000.
After Brexit, new applicants from EU countries will have to go through the same procedure, prompting fears of a large scientific skills shortage.
In response, Mr Johnson has asked the Home Office and Beis to develop a system that has no limit on numbers allowed to work in the UK under the tier one exceptional talent visas. He also wants them to expand the pool of UK research institutes and universities able to endorse candidates.
In addition, he wants officials to come up with criteria that confer automatic endorsement, subject to immigration checks, ensuring dependants are also able to work in the UK and remove the need to hold an offer of employment before arriving.
Prof Sir Venki Ramakrishnan, president of the UK's Royal Society, has been calling for such reforms since the result of the referendum on membership of the EU in 2016.
"We welcome the government's objective of supporting science by facilitating immigration of researchers at all levels, and look forward to discussing the details of a new immigration system," he told BBC News.
"But the fact remains, half of international academic talent in UK universities comes from the European Union and the EU is our single largest research collaborator.
"Alongside immigration reform, therefore, maintaining close working ties with researchers in Europe and access to EU research funding, are essential. A no-deal exit from the EU is the worst option for science."
Chi Onwurah MP, the shadow spokesperson on science and industrial strategy, said that a no-deal Brexit would be "hugely damaging" for British science.
"Britain is a science superpower and we need to build an innovation nation but that won't be achieved by a few fast track visas and re-announcing commitments already given, and broken, on replacement funding for EU programmes" she said.
"Science is a team activity, we need to promote collaboration at all levels not only the super-elite, and deliver on long-term commitments to be part of EU research programmes."
Mr Johnson reiterated that he did not want a no-deal Brexit but, were there to be one, he pledged to ensure that the UK would continue to collaborate in great scientific projects "under any circumstances".
"We are not only going to participate in the (EU funded) Horizon schemes, we in the new UK government are determined to finance big science as well," he said.
"So when these people come forward, as they are now, with plans for UK-generated fusion reactors, we are going to be championing those and supporting those as well."
The UK will be unable to participate fully in the EU-funded Horizon programmes once it leaves the EU and British scientists may not be able to be involved at all if the UK leaves without a deal.
Participation in Europe's programme to develop nuclear fusion, of which the Culham science centre is a part, will also be restricted after Brexit.
Devil in the detail
UK researchers are as much concerned about the loss of scientific collaborations with EU research institutes as they are about the loss of European funding.
A recent Royal Society study showed more than 33% of UK research papers are co-authored with EU scientists and countries associated to the Horizon 2020 research and innovation programme. This compares with 17.6% that are co-authored with US researchers.
James Wilsdon, professor of research policy at Sheffield University, described the proposed measures as "small beer compared to the chaos, disruption and damage to the UK's attractiveness to international collaborators & mobile talent that will result from a no-deal Brexit".
Dr Daniel Rathbone, assistant director of the Campaign for Science and Engineering (Case) welcomed the prime minister's "powerful message", but looked forward to seeing the details of his proposals.
"Any new visa system must be streamlined, easy to use and competitively priced compared to other leading science nations. Currently, UK visas are significantly more expensive than those of other countries.
"Science is also a collaborative enterprise, so it would be very beneficial if there was a streamlined process for these talented scientists to bring their teams with them to the UK."