Royal Bank of Scotland confirmed late last night the chief executive had decided to forgo the 3.6 million shares package worth £963,000 he was awarded last week.
The bonus has proved embarrassing for the Government with Labour pointing to David Cameron's pledges to clamp down on executive pay and Tory Mayor of London Boris Johnson claiming it was "absolutely bewildering" that a state-backed bank should pay out so much.
Chancellor George Osborne said: "This is a sensible and welcome decision that enables Stephen Hester to focus on the very important job he has got to do, namely to get back billions of pounds of taxpayers' money that was put into RBS."
Labour had planned to force a Commons vote calling for Mr Hester to be stripped of his bonus and claiming the Prime Minister's "failure of leadership" could not be allowed to stand.
Party leader Ed Miliband said Mr Hester "has done the right thing".
"It is a shame that a feeble, out of touch David Cameron did not realise he should do the right thing and stand up for the interests of the British people.
"Labour was right to seek a parliamentary vote on this so that the people's voice could be heard. But the debate about fair executive pay and responsible capitalism is only just beginning. We need a government that will tax bankers bonuses and bring responsibility to the boardroom."
Pressure intensified on Mr Hester after the bank's chairman, Sir Philip Hampton, announced on Saturday he would waive his payout.
He had been on course to claim 5.17 million shares in the financial institution in February, but it is thought he told the bank's remuneration committee it would "not be appropriate" for him to take a £1.4 million payout.
Mr Hester is still expected to be entitled to another shares bonus that could potentially reach £6.4 million based on a long term incentive scheme that is approaching the point at which it can come into effect.
Chairman of the Financial Services Authority Lord Turner, who said last week that excessive bonuses are "not good for society", will report to the Commons Treasury Committee on RBS today.
Scottish First Minister Alex Salmond said: "This is a welcome development but it should never have come to this stage as these circumstances cannot be left to individual decisions. They must be a matter of public policy.
"The sustaining of public services, and therefore economic recovery, requires pay restraint across the public sector.
"How can that be maintained against the background of huge bonuses being paid in organisations which are still within the public sector? This blatant inequality thus threatens economic recovery."
The First Minister added that both the coalition government and previous Labour government shared responsibility for the situation.
He said: "Labour negotiated the very deal with Stephen Hester that they have complained about while the coalition parties huff and puff about shareholder democracy but stand by idly when they carry responsibility for the public shareholding.
"They also have the option of a further tax on bonuses but instead all the Tory rhetoric is on reducing the top rate of tax.
"Collectively the Westminster parties display the complete abdication of responsibility of political parties out of touch with the public of both Scotland and England."
The TaxPayers' Alliance welcomed the move, saying Mr Hester's bonus would have been unacceptable.
Matthew Sinclair, the pressure group's director, said: "Taxpayers have seen the value of their investment in the bank fall by billions of pounds in the last year and are still a long way from getting their money back, so a million pound bonus for the boss there would be unacceptable."
He called for the bank to be put back into private hands as soon as possible.
Foreign Secretary William Hague stressed that Mr Hester's contract, including the long-term incentive element, was signed under the Labour government.
"As the Chancellor has said, it is a sensible and welcome decision," he told BBC Radio 4's Today programme.
"Stephen Hester has got to focus on the very important job that he has got to do."
Mr Hague said the coalition had already made "big changes" to curb the City bonus culture.
But he added: "I don't think we should rule out doing more as and when necessary."