A Department for Education technical notice published this week states that if the UK leaves the European Union (EU) with a deal in place then funding for the current programme, which runs from until 2020, will be unaffected.
However, if there is no agreement over the withdrawal of the UK from the EU then the government will need to negotiate with the European Commission to ensure British young people applying after the UK exits the EU on 29 March 2019 can receive funding.
If those negotiations fail then the UK government will need to negotiate with EU countries separately.
Erasmus+ offers opportunities for UK participants to study, work, volunteer, teach and train abroad in Europe. It also funds youth groups and services. Launched in 2014, the current programme is set to expire in 2020.
The government has clarified that it will underwrite funding for successful applications prior to the UK's departure from the EU, this includes those that are informed of their successful bid after that time.
The DfE is also recommending that applications for the 2019 Erasmus+ programme continue.
"This will ensure that organisations and individuals can take part in the programmes if a withdrawal agreement is in place," says a statement from the Erasmus+ UK National Agency.
Last summer, the DfE had indicated that in the event of a no-deal Brexit, awards made after the end of March could also be underwritten.
Further education group Universities UK is concerned that thousands of students could be denied government funding to study abroad in the event of a no-deal Brexit.
The group is particularly concerned that young people from low-income families and with disabilities could be hardest hit.
"Today's news from government provides welcome clarity for British students currently in Europe on Erasmus+ placements, as they should continue to receive funding for the duration of their time abroad," said Universities UK chief executive Alistair Jarvis.
"However, excluding any grants that may have already been agreed, government has not committed to new funding for study abroad placements beyond this.
"This means thousands of British students could miss out on the life-changing opportunity to take on placements at European universities on the Erasmus+ scheme.
"Students find themselves caught up in this political turmoil through no fault of their own. In particular, this decision will affect students from poorer backgrounds and disabled students, many of whom rely on financial help to meet the extra costs of studying abroad.
"As a matter of urgency, the UK government must reconsider its decision and commit to fund 2019/20 study abroad placements in the event of no deal."
The DfE's technical notice around Erasmus+ is one of a number of government updates on Brexit preparations.
This includes telling schools they can be flexible around the meals they serve in the event of food shortages caused by a no-deal Brexit. This update also asks schools to ensure that all free school meal entitlements are honoured.
Rob Percival, head of policy at organic food body the Soil Association, said a no-deal Brexit "would be a disaster for school meals for millions of children" as it would leave caterers struggling to provide healthy meals.