The widely-flagged move was confirmed today by Mr Osborne and is seen by many as a natural extension to the new pension freedoms which will arrive next month.
Mr Osborne acknowledged that selling annuities could be a complex process and that good advice was required to help make the right decision. He said the Government would consult on how to offer the appropriate advice although he made no mention of PensionWise.
Mr Osborne told MPs: "We will give five million pensioners access to their annuity. For many an annuity is the right product, but for some it makes sense to access their annuity now.
So we’re changing the law to make that possible.
"From next year the punitive tax charge of at least 55% will be abolished. Tax will be applied only at the marginal rate. And we’ll consult to ensure pensioners get the right guidance and advice."

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The annuity re-sale idea was floated by Pensions Minister Steve Webb to enable pensioners to re-sell existing annuity contracts, extending the pension freedoms to more people.
Some pension experts have warned, however, of the possible dangers of the proposals, with one saying they are "probably ill-conceived" and others warning that sharks will target pensioners to cheat them out of their annuity money.
Mr Webb said that retirees should be allowed to sell their annuities at any point to the highest bidder, generating a new market in second-hand annuities.
Claire Trott, head of technical support, Talbot and Muir, said on the sale of annuities: "The consultation formally announced in today's Budget on the sale of annuities is welcomed. It should be noted that it will be a complex area and should be regulated accordingly which again is welcomed. People could be hit by double charges, once when they took them out and once when they sell them on.
"They will have to go through substantial underwriting to ensure that the purchaser gets value for money, they will be making the offers so will be leading the rates payable. It is in the purchaser's interest to ensure they know enough about the annuitant's lifestyle to be able to make an appropriate offer."

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Steve Groves, chief executive of Partnership, commenting on the Budget, said: "This year's Budget contains good news for not only consumers but also for annuity providers.
"The creation of a well-regulated, carefully-designed, second hand annuity market could mean that peoples' annuities are now more flexible, still guaranteeing an income for life but also able to provide some extra cash when it is needed. It will provide those 5 million older people who have already taken an annuity with a greater degree of flexibility.
"Admittedly, the devil is in the detail and it now falls to the Government and industry to create a safe market which provides real value to consumers. Extending the freedoms to past-annuitants and providing future generations with even more flexibility is simply not good enough unless it has a genuinely positive impact on their lives and this needs to be at the heart of the consultation."