The government confirmed the UK will contribute approximately £570m to the scheme to cover the 2027-28 academic year.
It said it had secured a 30% discount on what it would have paid under its current trade agreement with the EU, which encompasses many other industries.
The EU Relations Minister said it was a “huge win” for young people and will ensure everyone has the opportunity to study and train abroad.
“This is about more than just travel,” said Nick Thomas-Symonds.
“It’s about future skills, academic success, and giving the next generation access to the best possible opportunities.”
Royal Society of Edinburgh’s president and former principal of Glasgow University Sir Anton Muscatelli said he welcomed the UK government’s decision.
“Anyone who has ever studied abroad will attest that the connections and collaborations fostered through international study reap benefits for many years,” he said.
“Erasmus also opens up Scotland to students for all over Europe to come to here and experience the world-class higher education and excellence in research that our nation has to offer.”