The changes, which would come into effect for those starting undergraduate courses or above in 2020/21, represent a loosening of the rules introduced by the then home secretary Theresa May in 2012, which stated that overseas students had to leave within four months of finishing their degree.
The extension would be conditional on the students studying at institutions with a track record in upholding immigration checks.
However Migration Watch UK described the move as an “unwise” and “retrograde” step which would “likely lead to foreign graduates staying on to stack shelves, as happened before”.
Chairman Alp Mehmet said: “Our universities are attracting a record number of overseas students so there is no need to devalue a study visa by turning it into a backdoor route for working here.”
The announcement of the rule change by Boris Johnson coincided with the launch of the world’s largest genetics project, the £200m 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.”
The new rules are being seen as a particular boost for the so-called STEM subjects – Science, Technology, Engineering and Maths – where international students account for half of all full-time post-graduates.
Home Secretary Priti Patel said: “The new Graduate Route will mean talented international students, whether in science and maths or technology and engineering, can study in the UK and then gain valuable work experience as they go on to build successful careers.
“It demonstrates our global outlook and will ensure that we continue to attract the best and brightest.”