Academics from the EU must be given guarantees over their future to prevent a "brain drain" of talent, MPs have warned.
Brexit has created "significant uncertainty" for university staff and students, and the international success of the UK's universities could be put at risk if government does not address concerns within the sector, according to the Commons education select committee.
In a new report analysing the impact of the UK leaving the EU on higher education, the committee warns that the rights of EU university staff to work and live in the UK must be guaranteed as soon as possible.
EU workers make up around 16% of the UK's university workforce, the report says, with the numbers growing by over 10,000 in the last six years.
But it notes that a recent survey showed that over three-quarters (76%) of European academics at UK universities said they are likelier to consider leaving UK higher education due to the referendum result.
Meanwhile, another poll of academics found that 53% of non-UK nationals were actively looking to leave the UK.
The Government must quickly resolve the issue of EU academics' rights to live in the UK, the committee warns.
It says: "The Government has rightly identified the agreement of the rights of EU nationals as its first priority in the negotiations.
"However, we caution that a delay in confirming these rights will only intensify the current uncertainty for universities, and likely lead to a significant 'brain drain' in talented staff."
The rights of EU nationals must be unilaterally guaranteed by government before the end of the year, if a reciprocal deal is not reached before then, it adds.
The committee also calls for a new "easier" visa route for academics worldwide, with less bureaucracy, to help attract workers to the UK.
In 2015/16, 5.6% of students at UK institutions were from the EU, and a further 13.6% were from non-EU countries, the report says.
EU students generated an estimated £3.7 billion for the UK economy in 2011/12.
It is important that universities are given enough notices of any changes to EU students' migration status and their access to fees and loans, the committee said, so that they can plan ahead.
Last week, the Government confirmed that EU students starting courses in autumn 2018 would still be eligible for the same loans and grants as UK students, and for the duration of their course.
In the future, the committee says, it believes that the best plan for EU students is to keep a "reciprocal open approach with light touch controls, such as visa-free access", to retain a system "closely resembling freedom of movement". This approach should be taken with all international students.
The Government should remove overseas students from the net migration target to make it clear it wants talent from across the world to come to the UK, it adds.
Committee chairman Neil Carmichael said: "Higher education in the UK is a world leader but Brexit risks damaging our international competitiveness and the long-term success of our universities.
"It's welcome that EU students have been given some guarantees on their funding and loan access but the Government must act urgently to address the uncertainty over EU staff and avert the risk of a damaging 'brain drain' of talent from our shores.
"As we leave the European Union we now have the opportunity to reform our immigration system to ensure we reap the full rewards of the ability of our universities to attract the brightest and best students and staff from across the world."
Sally Hunt, general secretary of the University and College Union, said: "As well as removing international students from net migration figures, government must guarantee the rights of EU citizens currently working in the UK.
"Along with international students, overseas staff make a huge contribution to UK society and I call on the Government to end their uncertainty or risk damaging the UK's ability to attract staff and students from around the world."
Alistair Jarvis, deputy chief executive of Universities UK, said: "The committee is right to identify European staff, immigration policy and research collaboration as priorities for universities as Brexit negotiations start.
"The Government should seek to secure continued close collaboration with EU research partners and also provide certainty for EU staff currently working in UK universities in terms of work and residency rights.
"Changes to our immigration system are also needed to ensure that the UK remains a destination of choice for international talent and students."