Video report by ITV News Deputy Political Editor Chris Ship
David Cameron has secured support from all other EU leaders for new flexibility on VAT which would allow the UK to introduce a zero rating on sanitary products such as tampons.
UK officials said that the European Commission has signed up to the change and will put forward proposals next week.
A formal announcement is expected on Wednesday, though the implementation of new rates may take some time to be approved.
The development came after the Government learnt it was facing a Commons revolt by Tory MPs demanding it acts unilaterally to withdraw the charge - in defiance of EU rules.
Stella Creasy, the Labour MP for Walthamstow, told ITV News that it was "about time" that tampons were recognised as a basic necessity.
She hailed the step forward on the issue but stressed no final deal had yet been done.
The MP also questioned whether women's charities would still receive millions of pounds they had been promised from the funds raised through tampon sales.
Elsewhere, campaigners reacted with delight to the news, while Eurosceptics said that the issue showed how much Britain was in thrall to Brussels.
Laura Coryton, from campaign group Stop Period Tax, told ITV News it was an "important day" for those who had campaigned for the change:
Chancellor George Osborne hailed the agreement tonight as he said that the government "heard people's anger over paying the tampon tax loud and clear".
Mr Cameron had decided to force the issue over the tampon tax by raising it at a summit of the European Council in Brussels. He first spoke to Commission president Jean-Claude Juncker and then asked fellow leaders to include a commitment in the official conclusions of the two-day meeting.
The 28 leaders agreed unanimously to a statement welcoming "the intention of the Commission to include proposals for increased flexibility for member states with respect to reduced rates of VAT, which will provide the option to member states of VAT zero-rating sanitary products".