An Isa-style scheme would have ended tax relief on contributions, but made pension pot withdrawals tax free.
Mr Osborne was due to unveil the plans in the Budget on 16 March, but was warned it could cause a run on savings.
The proposal, which would have made savings from the government’s £21bn tax relief bill, had been opposed by pensions minister Baroness Altmann.
Conservative MPs had also become concerned about the impact of the changes on higher earners.
A Treasury source said now was not the time to make changes to pension tax relief.
BBC political correspondent Eleanor Garnier says the decision is a recognition of how fragile the EU referendum campaign is – avoiding the changes removes the risk of upsetting voters ahead of the vote in June.
The chancellor had been considering two options – the other being a flat rate of tax relief for everyone saving for a pension. Those who pay higher rates of tax currently get bigger breaks.
An ally of the chancellor told the Times: “George has always been clear he wouldn’t do anything to damage saving.
“He’s listened to what people have said and concluded that now isn’t the right time, with uncertainty in the global economy and reforms such as auto-enrolment still bedding in, to turn things on their head.
“It is also clear that employers wouldn’t welcome a wholesale change in the way they administer schemes. So he is not going to tear up the system of pension tax relief. There won’t be any changes to tax relief at all in the budget.”
Baroness Altmann made clear she was opposed to the idea, and there was the threat of resistance from Tory MPs worried about the effects on their constituents, potentially costing higher-rate taxpayers thousands of pounds from their retirement income.
The pensions minister said: “The freedom and choice reforms have put us in a place where people’s pensions can work well for them.
“However, tax is a natural brake on them spending their pension fund too soon.”
How pension tax relief works
Pension tax relief is given on contributions at the rate of income tax – 20%, 40% or 45%.
Someone at the 20% rate contributing £10,000 gross to their pension would have to pay £8,000 net, at 40% it would be £6,000, and £5,500 for those at 45%. So it favours the better off.
Pension savers currently pay no tax on money they put in but pay tax on the cash they take out above their personal allowance.
The amount anyone can save into a pension and get tax relief is capped at £40,000 annually and £1.25m in their lifetime.
The proposal had been opposed by the pensions industry.
Yvonne Braun, of the Association of British Insurers, said the scheme would have hit current savers and could have created a “fiscal time bomb” for future generations.
She said: “Many savers would be worse off and it would also damage the economy more widely because of its impact on saving and investment.”
Changes to the pensions system in recent years have included automatic enrolment into workplace pensions in 2012 and people aged 55 and over being allowed to take their retirement pots how they want rather than being required to buy an annuity retirement income introduced in 2015.