The orchestra was on the brink of closure two years ago because of funding cuts.
However, it received a last-minute deal from Stormont and Belfast City Council.
Sir George, who is stepping down as chair later this week, said the orchestra's financial situation has greatly improved.
"Two years ago, to use an accounting term, we weren't sure we we were going to be able to say it was a going concern - that is that you could look ahead 12 months and say you were going to be solvent," he said.
"This year, already, we know that we're going to be getting funding from government sources that will make our future secure."
The orchestra is the only full-time professional orchestra in Northern Ireland.
It plays the majority of its concerts in Belfast's Ulster Hall and the Waterfront Hall.
The outgoing chair of the Ulster Orchestra, Sir George Bain, says the organisation's future is more secure than it has been for a very long time.