Last week’s announcement that Hester would receive £963,000 in shares, a decision approved by the RBS board, led to a public outcry and demands that the government should block it.
The Labour Party had also been vocal in its opposition and had indicated it would force a vote on the issue in Parliament.
However, Hester will now reject the bonus, which was to be paid in shares, the BBC has reported.
The Chancellor George Osborne said it was “a sensible and welcome decision”.
On Saturday, it was revealed that RBS chairman Sir Philip Hampton had given up a £1.4m shares reward he was due to receive next month after he came to the conclusion it would not be appropriate.
Since the announcement of Hester’s bonus on Friday, the government had been reluctant to intervene, claiming it was part of his contract, drawn up under the Labour government.
