The Chancellor had been reportedly considering unveiling plans to make pensions more like Isas in the Budget on March 16.
But experts had warned it would hit savers and could trigger a crisis with savers rushing to withdraw their retirement funds.
The idea was mooted in 2015 and a consultation into pensions tax relief was launched last summer - but experts warned that if such a move happened it could lead to a Northern Rock-style run on the system.
An Isa-style system would have removed the up-front tax relief on contributions, but allowed withdrawals to be made tax-free instead.
But doing so could mean people feel less inclined to keep their money in their pot, experts warned.
A Treasury source confirmed Mr Osborne had ditched the proposal because he had “always been clear he would not do anything to damage saving”.
The proposals had also faced resistance from Tory MPs and It is understood that there will not now be changes to pension tax relief in the Budget.
The pension system has already undergone a huge series of shake-ups in recent years, with the introduction of automatic enrolment into workplace pensions in 2012 and the pension freedoms launched in 2015 which allow people aged 55 and over to take their savings pots how they wish, rather than being required to buy an annuity retirement income.
Pensions Minister Baroness Altmann told the Financial Times: “The freedom and choice reforms have put us in a place where people’s pensions can work well for them.”
In comments seen as a warning to Mr Osborne not to change the current regime Baroness Altmann, a former consumer campaigner, continued: “However, tax (applied to pension income under the current system) is a natural brake on them spending their pension fund too soon.”
Yvonne Braun, director of long term savings at the Association of British Insurers (ABI), said: “The pension Isa would hit today’s savers and could create a fiscal time bomb for future generations.
“Many savers would be worse off and it would also damage the economy more widely because of its impact on saving and investment.”
Tom McPhail, head of retirement policy at Hargreaves Lansdown, said: “An Isa-style reform with tax relief being scrapped in favour of tax-free withdrawals would create the risk of a future Northern Rock-style run on the pension system and the UK stock market.
“Any hint of political interference in the future could result in billions of pounds being withdrawn overnight; it would be hugely unstable.”
Former pensions minister Steve Webb welcomed the Chancellor’s decision but called on him to guarantee there would be no changes on tax relief until at least 2020.
Alongside the Isa-style reforms, an alternative option was to set a flat rate of tax relief - something which many Tories feared would have been unpopular with higher earners.
The Liberal Democrat, now director of policy for Royal London, said he backed a flat rate but now was not the time for further upheaval.
He told the BBC: “There is a case for reform, for giving everybody the same generous rate of relief. One of the worries was that the Chancellor wouldn’t just take the existing pot and just reallocate it but he would take billions out - there really are tens of billions of pounds at stake in tax relief.
“Given that we are actually not saving enough, we need more help to save for our pensions, one of the big fears was that this would all be about the hole in the budget not about promoting long-term saving.”
He added: “My plea to the Chancellor would be, on Budget day, tell us you are leaving it alone at least for a parliament so people can actually plan for the long term.”
Richard Parkin, head of pensions at investment firm Fidelity International, said: “The threat of radical change to pension tax relief appears to have receded for now but the problems identified in the Chancellor’s review and the subsequent national debate remain.
“We expect this is action postponed rather than action abandoned. We should use this time to have a fuller and less hurried debate of how best to support long term pension saving. We already have changes coming into effect for higher earners in April that are causing significant disruption and we urge the Chancellor not to fiddle with the system further.
“If we are to make changes then let us do that in a considered and orderly way rather than continuing the tinkering that adds complexity and undermines public confidence in the pension system.
“We would still urge consumers to make the most of the current system while it is still in place - this is a postponement and not a cancellation of change.”