The European Commission has proposed opening negotiations with the UK to allow mobility enjoyed before Brexit to millions of 18- to 30-year-olds in a major concession.

It said it would now seek approval from individual EU leaders to start the talks, which could partly eliminate one of the most controversial elements of Brexit, a block on the right to live in one another’s countries, albeit for a limited period and with conditions.

Referring to the post-Brexit trading agreement on Northern Ireland, the commission president, Ursula von der Leyen, said: “Since we have the Windsor agreement in place, the relationship has been much more constructive.

“There are certainly topics where we can have closer collaboration … and the topic of youth mobility is in both our interests because the more we have youth mobility being on both sides of the channel, the more we increase the probability we will be on good terms because the next generation knows each other very well.”

Under the envisaged agreement, EU and UK citizens aged between 18 and 30 would be able to stay for up to four years in the destination country, the European Commission said in a detailed statement.

If agreed, a youth mobility scheme visa would be issued in those countries that participate, with possible conditions including a requirement for health insurance and proof of sufficient subsistence funds, a feature of other mobility schemes around the world.

“The objective would be to facilitate youth exchanges, making it easier for young EU citizens to travel, work and live in the UK, with reciprocity for young UK nationals in a member state,” the commission said.

The decision by the commission, which has in the past been vehemently opposed to making any concessions to the UK sought since Brexit, is seen as a breakthrough in UK-EU relations.

The proposal to open negotiation must first be agreed by EU leaders. Sources say the first opportunity could arise in May at a meeting of general affairs ministers.

If approved, it would mean millions of young people could come to the UK to fill the gap left by Brexit in the hospitality sector, and also in universities. It would mean seasonal work, from restaurant work to jobs in ski resorts, would be available again to British young people in EU countries.

It may also make it easier for UK and EU universities to recruit researchers, particularly those involved in the Horizon science research programme. Under the scheme it is also envisaged that the university student home-fee system would be restored in both directions, ending the crippling overseas fees which sometimes amounted to more than £40,000 a year.

The Swedish minister for European affairs, Jessika Roswall, told the Guardian: “Sweden has pushed for this and we feel this is very important for the youth and students in the EU and the UK, they are the winners.”

In its announcement, thecommission said it had acted after the UK had made approaches to individual EU countries, known to include France, to open a youth mobility scheme.

UK ministers have argued that it would not be a backtracking on one of the key elements of Brexit, the end of free movement for British citizens. They argued that France already had such an agreement with Canada, and Australia had a similar deal with the UK, and that it would be an important way to foster cultural exchange for future generations.

“Mobility would not be purpose-bound, ie beneficiaries should be able to undertake different activities during that period, such as studying, training, working or travelling, neither would mobility be subject to a quota system,” said the commission.

Kate Nicholls, the chief executive of UKHospitality, said: “We have been calling for these schemes to be expanded and I’m pleased to see the EU Commission coming to the table with a plan to open negotiations. I hope the EU Council agrees with the proposal and that talks between the UK and EU can begin as soon as possible.”

The commission’s statement raises a possibility that it could pave the way for university places in one another’s countries if member states and the UK saw fit. And agreement “would also provide for equal treatment (ie, non-discrimination) between EU and UK citizens in respect of higher education tuition fees”, the statement said.

The commission stressed that a youth mobility scheme would not be reinstating free movement as it would come with conditions including a limited stay in one another’s countries.

“The envisaged agreement would provide for limited-in-time mobility, subject to the fulfilment of conditions to be checked before the mobility can take place. The conditions should also be met during the stay. It is not about conferring to young UK nationals the benefits of the fundamental freedom of movement enjoyed by EU citizens,” it said.

It added that Brexit had particularly “affected the opportunities for young people to experience life on the other side of the channel and to benefit from youth, cultural, educational, research and training exchanges”.

It also said that a bloc-wide deal was preferable to a series of bilaterals as it would ensure equal treatment for every person in the scheme.

Lord Kinnoull, the chair of the House of Lords European affairs committee, which recommended such a mobility programme, welcomed the development, saying if agreement was reached it would be “greatly to the mutual benefit of both parties and to the youth of Europe”.