The cuts are expected to be spread around the bank's offices across the world, but it is feared some workers in the City will lose their jobs as the global investment arm is decreased from 11,000 to 9,000.
Mr Hester will leave later this year and will receive 12 months' pay and benefits worth £1.6 million and the potential for a £4 million shares windfall from a long-term incentive scheme. But he will receive no bonus for 2013.
He said: "We are now in a position where the Government can begin to prepare for privatising RBS. While leading that process would be the end of an incredible chapter for me, ideally for the company it should be led by someone at the beginning of their journey."
Chancellor George Osborne said Mr Hester should be commended for "having brought RBS back from the brink" following its taxpayer bailout at the height of the financial crisis.
He said: "When Stephen Hester took on the job at RBS in 2008 it was a bust bank with a broken culture and posed a huge risk to financial stability. RBS today is safer, stronger and better able to support its customers. I want to commend Stephen Hester for everything he has done to make this turnaround possible."
Mr Hester told reporters it had been the board's choice for him to make way for someone new to lead the bank through privatisation and that he had been prepared to carry on.
He said he was "co-operating amicably and will stick around as long as they need me" before going on holiday. But he admitted having "some human regrets" about not completing the bank's transition to private markets. RBS has launched a search for his successor and Mr Hester will continue in his role until December, unless a successor is in post earlier.
"I have been pretty clear that I suppose I feel torn about this - I feel a sense of loyalty to the company and I want to do what is right for the company. If that was to lead the company through privatisation, I wanted to do that."