The 51 year-old believes that since he became chief executive in November 2008 the bank has been taken from "sub-par" to performing in line with other similar businesses.
And while he is expecting a "tough slog" of a recovery he is hopeful the major parts of the turnaround of RBS remain on course to be completed by the end of next year.
Mr Hester, who will be meeting bank customers in Glasgow today, said: "The coming years will be about taking these ongoing businesses and making them more than healthy, making them really good so we can be a really good bank.
"Of course that is something that will take us many years.
"As the restructuring phase goes away people will be able to see us more like a normal bank.
"Some of the disfiguring big numbers of losses will be taken away and we will be able to see more clearly what we already do to support our customers and the improvements we intend to make.
"I hope that in turn will provide the opportunity for the Government to use taxpayers' money more productively than having it tied up in our shares and that privatisation will take place."
The issue of the timing of the sale of the Government-owned stake is, Mr Hester says, one for the political leaders.
However, he is adamant that when the day comes it will be a "terrific" signal of recovery in the economy.
He said: "These are gargantuan sums of money that taxpayers have had tied up in a bank that are better either to be given back to taxpayers or used in whatever way taxpayers prefer for it to be productive in the economy."
This year RBS has repaid the near £200 billion of the emergency liquidity support it took during the financial crisis.
Mr Hester also hopes to shortly announce RBS's exit from the asset protection scheme.
The £300bn of insurance provided by the UK Government has not been needed but the public purse will record a £2.5bn profit from offering the scheme to the bank.
Mr Hester said: "These are really big moves in helping the Government redeploy its money away from things to do with banking while we deploy our money to things to do with banking and supporting our customers."
Without any trace of self-pity Mr Hester, sitting in an RBS office in St Andrew Square in Edinburgh, admits his job can be difficult.
The tens of thousands of people made redundant by RBS in the past four years is a human cost to the major restructuring which has seen the bank's balance sheet shrink by more than £700bn.
He said: "I don't think toughness is restricted to the size of enterprise you manage. You can have a good or bad day whatever you do in life and have things you worry about.
"We went for a period when we were an unsuccessful business so that meant we had to shrink and we employed less people.
"We also have a duty if we are to serve our customers well to make our services affordable and that means we have to be efficient.
"All of us have to juggle challenges. As far as I can see the best way through is if you serve your customers as well as possible they will do more business with you and then you will be an expanding rather than a shrinking business. That is the point when we get to employ more people."
During his visit to the Scottish capital Mr Hester met with entrepreneur Elizabeth 'Liggy' Morgan who set up her cupcake-making business, Liggy's Cakes, in 2007 and who now has one shop in Edinburgh and one in Bearsden.
Mr Hester said it was always inspiring to meet young people bursting with ideas and who had set up their own business.
RBS also announced it was investing £1 million over the next three years in funding and mentoring of younger entrepreneurs.
Initiatives include extending a partnership with The Prince's Trust, additional support for Youth Business Scotland, a new three-year agreement with the Entrepreneurial Spark organisation and an extension of funding to the RBS university enterprise programme.
Mr Hester said: "Big businesses start from small ones so this showcases what we do to help others help small businesses as well as helping them directly and also increases what we do in that area."
Almost four years in to his tenure at RBS, Mr Hester, 51, remains fully focused on restoring the bank's reputation although he is under no illusions it will be easy.
He added: "I've always thought there was a really good bank that could come out of a bad situation. That is what has given me and all my colleagues around the bank the energy and fortitude to come through bad times.
"That said I think it would be wrong to think we are out of the difficult times. We are still in a difficult moment for society and economies.
"Even if the economy recovers, as I believe it will, I think there will be months and possibly years where it will feel a bit like hard work along that path.
"It is not likely to be an environment where we are likely to be springing free and saying how wonderful it is our problems have disappeared."
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