Laws limiting how long foreign students can stay in the UK after graduating are to be relaxed.
International students will be able to remain in Britain for two years after graduating, to find work.
The Prime Minister said the changes, due to come into effect for those starting courses next year, would help those studying in the UK begin their careers in the UK.
It marks a shift in policy designed to add flexibility to the system for graduates from the era, when student numbers were included in overall targets.
The announcement coincides with the launch of the world's largest genetics project, the £200 million whole genome sequencing project in the UK Biobank, which aims to transform genetic research.
Mr Johnson said: 'Britain has a proud history of putting itself at the heart of international collaboration and discovery.
'Over sixty years ago, we saw the discovery of DNA in Cambridge by a team of international researchers and today we are going even further.
'Now we are bringing together experts from around the globe to work in the UK on the world's largest genetics research project, set to help us better treat life-threatening illnesses and ultimately save lives.
'Breakthroughs of this kind wouldn't be possible without being open to the brightest and the best from across the globe to study and work in the UK.
'That's why we're unveiling a new route for international students to unlock their potential and start their careers in the UK.'
Business secretary Andrea Leadsom said Government proposals to allow international students to stay in the UK for two years after graduating was 'absolutely in the UK's interest'
International students who have successfully completed a course in any subject at an institution with a track record in upholding immigration checks will be able to benefit from the measures.
They will apply to students who start courses in 2020/21 at undergraduate level or above.
The proposals cover international students who start courses in 2020/21 at undergraduate level or above.
It is understood it will also apply to those already on higher education courses with Tier 4 visas (a general student visa) when the changes are introduced.
But this means it is not expected to apply, for example, to those currently studying in the UK and due to graduate next year.
Latest figures show that in 2017/18, there were around 319,000 international students, from countries outside of the European Union, studying undergraduate and postgraduate courses at UK universities.
Tens of thousands start courses, and graduate, each year.
Stephen Isherwood, chief executive of the Institute of Student Employers, welcomed the move, but said "we would like to see students who graduate in 2020 eligible for the visa".
He added: "This will allow ample time for universities, students and employers to understand and implement the new rules."
Nick Hillman, director of the Higher Education Policy Institute (HEPI), said that while it would have been beneficial if the change had applied to current international students, the fact that it applies to future generations is not "catastrophic".
"It would have been good if this had been applied retrospectively, but nobody has been misled about anything," he said.
The move was welcomed by Chancellor Sajid Javid, who as home secretary under Mrs May is known to have clashed with her over immigration quotas.
He tweeted: 'About time. Should have reversed this silly policy years ago.
'Britain should always be open to the best talent from across the world.'
Business secretary Andrea Leadsom said Government proposals to allow international students to stay in the UK for two years after graduating was 'absolutely in the UK's interest'.
She told BBC Radio 4's Today programme: 'Graduates very often when they first finish their degree, they look around for a job and it takes them a little while to settle into the world of work and therefore giving them that two-year period will enable them to find a job that befits their degree and that enables them to then use the work route.'
Shadow home secretary Diane Abbott said: 'Labour has always said graduates should be able to work here after their studies because it enables them to contribute to our economy, our universities and to research, and helps us to attract the brightest and best from around the world.
'It is a great pity that ministers have previously supported measures that did the opposite.
'But it also highlights the foolishness of Government plans to place a salary limit on work visas at £30,000.
'Many of the graduates doing fantastic medical and other research earn less than that.
'Government policy will prevent us from attracting them to live and work here.'
Compiled by Olalekan Adeleye