The government has begun inviting applications for the Turing scheme, which enables students to study in other countries.
The scheme is named after the mathematician Alan Turing, and replaces Erasmus, a European Union (EU) programme which UK students can no longer take part in.
The UK turned down the an offer to continue participating in Erasmus after Brexit.
Universities minister Michelle Donelan said the Turing scheme would "enable up to 35,000 students throughout the UK to work or study across the globe".
What is the Turing scheme?
The new scheme will provide funding "towards placements and exchanges" of students.
Universities and other organisations in the UK can apply for grants to help cover travel expenses and costs of living as well as the administrative costs of running the scheme.
Applications have to be made by bodies such as universities, further education colleges and schools. If they are successful, these bodies can invite their own students to apply for individual funding.