A statement from the taxpayer-backed lender said the chief executive would receive a bonus of £963,000.
But the bank admitted he would still be eligible for up to £4.8 million under a long-term incentive plan (LTIP).
When added to his £1.2 million salary and £420,000 pension, his pay for last year could total £7.38 million.
General Secretary of the Rail Maritime and Transport union, Bob Crow, said: “The Royal Bank of Scotland is owned by the country. To give someone £1m and then to give them a massive bonus on top, while public sector workers get a pay freeze and their pension contributions go up, I have got to say that is a complete disgrace.
“What a kick in the face to those people who deliver a public service for our people in this country.”
Eighty per cent of the bank is owned by UK taxpayers and the company that runs it for the government said the bonus showed Hester’s work “towards rebuilding RBS”.
If Hester receives the maximum LTIP grant this year, he will have received a total of £27.5 million from the award since he was made chief executive in October 2008.
But because RBS’s share price has collapsed in the last 12 months, the actual value is likely to be lower.
Political pressure has mounted in the last two weeks for Hester’s annual bonus – which could have been £1.66 million – to be cut.
Jeremy Browne, the Foreign Office Minister said the bank chief earned in three days the equivalent of one year’s pay for a soldier in Afghanistan.
He added: “He is working for a company which is five sixths owned by us, the taxpayer, and I think he has to think like a public servant, not like someone who’s there to line their own pocket.
“He needs to think like a public servant who has a duty to his country, not just his own wealth.
“No-one’s forcing him to take this money. He could struggle on with £1.2m.”