This means that those who have invested in an income for life in their pension will be able to reverse the deal.
The government did say, however, that they would aim to bring in safeguards so to help people with the decision-making process.
Baroness Ros Altmann, the Pensions Minister, said that for the majority, keeping their annuity would be the correct decision.
The government states that in the UK, around five million people have invested in annuities, receiving a total income of £13bn each year.
Although it is still possible to sell an annuity right now, the tax stamp of between 55% and 70% puts many people off.
The proposed changes include a tax change – the person who is selling their annuity will only be charged at their highest marginal income tax rate.
Another rule being introduced is that insurance companies will be able to buy back annuities from its customers.
To ensure customers get the best deal they can, the government has said that this will be done through an intermediary.
All people who have invested in private pensions were previously obliged to use their pension pots to purchase an annuity.
The rules introduced this year enabled pension savers to choose what they do with their pension pot – i.e. they could take it out in one lump sum if they so wanted.
The rules, however, did not affect those who has already purchased an annuity.
The new rules coming in April will allow someone who has an annuity to sell it for a lump sum. This will probably be to an authorised buyer or an insurer.