The SNP is claiming victory after a Government "U-turn" meant international students will be able to stay in the UK to find work for two years once they have graduated.
Prime Minister Boris Johnson said the changes, due to come into effect for those starting courses next year, would help those studying in Britain to begin their careers in the UK.
Post-study work visas were abolished by the Conservative-Liberal Democrat coalition government in 2012, meaning any graduates wishing to stay in the UK had to apply as a worker.
The SNP had been among those calling for its reintroduction ever since it was closed.
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But the new policy - known as the "graduate route" - has been described as "long-overdue" and concerns have been raised as to whether the policy will meet "Scotland's specific needs".
SNP MP Stuart McDonald said: "This screeching Tory U-turn is a huge victory for the SNP, Scottish Government and Scotland's education sector.
"We have been campaigning hard for the reintroduction of the post-study work visa ever since the Tory-Lib Dem coalition government's damaging decision to scrap it in 2012.
"This long-overdue move underlines the absurdity of this shambolic Tory Government, and their harmful and erratic hostile environment policies.
"The devil will be in the detail as to whether this proposal is a full replacement and meets Scotland's specific needs.
"Having now accepted the decision to scrap the post-study visa was wrong, the Tories and Lib Dems should apologise for the damage they have caused by deterring international students from coming to live, work and contribute to Scotland.
"Westminster has consistently failed Scotland when it comes to immigration policy. It is clearer than ever that the only way to properly protect Scotland's interests - and build an immigration system that truly meets Scotland's needs - is to become an independent country."
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International students will be able to benefit from the new measures if they have successfully completed a course in any subject at an institution with a track record in upholding immigration checks.
They will apply to students who start courses in 2020/21 at undergraduate level or above.
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.
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Mr Johnson said: "Britain has a proud history of putting itself at the heart of international collaboration and discovery.
"Over 60 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."
Scotland's Minister for Further and Higher Education Richard Lochhead said:
"This is a welcome step forward but only one of many measures required.
"It should not have taken seven years for the UK Government to accept the arguments from partners across Scotland and reverse their decision.
"It is clearer by the day that Scotland urgently needs a migration policy tailored to our distinct needs and for the devolution of powers to develop, deliver and maintain policies that meet the needs of Scotland's universities, communities, public services and economy."
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