Prime Minister Keir Starmer had suggested in May that a youth mobility scheme could be part of a new deal with the EU.
The BBC understands that UK students will be able to participate in the Erasmus scheme from 2027.
Alex Stanley, from the National Union of Students (NUS), said it was “fantastic that another generation of students will be able to be part of the Erasmus programme”, adding that it would represent “a huge win for the student movement”.
“Students have been campaigning to rejoin Erasmus from the day we left,” he said.
The Erasmus scheme was scrapped in the UK in December 2020, when the government announced its post-Brexit trade deal with the EU.
Boris Johnson, prime minister at the time, said it was a “tough decision”, but the scheme had become “extremely expensive”.
He said it would be replaced by the Turing scheme, which has operated since then.
Both schemes are open not just to university students, but also to people doing vocational courses, as well as apprentices and people training at college or school.
In 2020, the last year in which the UK participated in Erasmus, external, the scheme received 144m euros (£126m) of EU funding for 55,700 people to take part in Erasmus projects overall.
The UK sent out 9,900 students and trainees to other countries as part of the scheme that year, while 16,100 came the other way.
Glasgow, Bristol and Edinburgh were the three universities to send the most students, and Spain, France and Germany were the most popular countries which UK students went to.
In the 2024/25 academic year, the Turing scheme had £105m of funding, external, which paid for 43,200 placements, with 24,000 of those being in higher education, 12,100 in further education and 7,000 in schools.
The majority (38,000) were from England, with 2,900 from Scotland, 1,000 from Wales and 1,200 from Northern Ireland.
Ministers who introduced the Turing scheme in 2021 said it was designed to benefit more people from disadvantaged backgrounds, external and provide greater support for travel costs than the Erasmus scheme did.
It is not yet clear what will happen to the Turing scheme once Erasmus is reintroduced for UK students.