The government was facing a rebellion from Eurosceptic MPs over the 5% VAT rate on women's sanitary products.
It is at the lowest rate allowed by EU law but rebels unhappy with EU say over tax rates were set to join forces with Labour to insist on VAT being removed.
Labour leader Jeremy Corbyn said it was "another Labour victory" on the Budget.
The government has also conceded ground over the issue of VAT on solar panels and other domestic energy saving and insulation products, amid a threatened Conservative rebellion over a potential tax rise.
VAT is currently charged at the reduced rate of 5% on sanitary products - but more than 300,000 people have signed a petition calling for sanitary items to be exempted from tax altogether.
In Wednesday's Budget, Mr Osborne said he recognised public feelings about the issue and said the EU had agreed to give the UK the leeway under EU law to set a zero rate.
Hailing what he said was a tax concession from Brussels that "no British government has even tried to achieve", he pledged to spend the proceeds of the tax on women's charities.
The government has now confirmed it will not oppose a Labour amendment to the Finance Bill calling for a zero rate of VAT. A number of Conservative MPs had threatened to vote with Labour on Tuesday to highlight the role of Brussels in setting VAT rates.
Some of those say they still intend to do so, arguing they think implementation of the reduced VAT rate will be delayed while all other 27 EU countries agree to the changes.
Labour MP Paula Sheriff, who tabled the amendment, welcomed the news. She tweeted: "Wow, thank you. Happy being the MP for Dewsbury." Labour leader Jeremy Corbyn described it as "another Labour victory".
At last week's European Council summit in Brussels, the 28 leaders agreed 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".
The European Commission has said it is working on two options that would allow member states more flexibility over setting VAT rates and will set out proposals on Wednesday.
Ministers have said they will not oppose calls to scrap the so-called "tampon tax" when the issue comes to a vote in the House of Commons.