Mr Orr has been chief executive of the company which has gold operations at both Macraes, in East Otago, and Reefton, on the West Coast.
He oversaw the start of the Didipio project, in the Philippines, but that was mothballed.
The company is optimistic the project will be restarted sometime in the future.
Oceana Gold said in a statement that chairman Jim Askew would become executive chairman until a new chief executive was appointed.
"The chairman and the board thank Steve for his five years of service to Oceana Gold.
Under his tenure, Oceana Gold has built two additional mines in New Zealand, increased production to 300,000 ounces a year, and become the fourth largest Australasian gold producer."
Since commissioning the new mines, the operational performance of the company had improved consistently over the last four quarters, the company said.
The Didipio project had been redesigned to benefit from changed market conditions.
ABN Amro Craigs broker Peter McIntyre said the Didipio project was likely to be a "cash cow" for Oceana Gold in the future, but the company had been hampered in financing arrangements because of the credit crisis.
The company had been using the New Zealand operations to prop up the whole business.
That had put Oceana Gold at risk for working capital.
New Zealand was also a much safer mining environment than the Philippines.
"It must be frustrating for the board to see Didipio stalled."
ABN had previously said Oceana Gold should consider taking on a joint-venture partner or raising more cash.
Mr McIntyre said mining was a rough and tumble business and five years in the top job was a "good duration" in the industry.
The only surprise was that Mr Orr was leaving before Didipio was completed.
"For all we know, he might have been head-hunted away."
Oceana Gold's share price had risen substantially recently.
The company was over-sold and the strong rebound in gold prices had seen buyers return to the sector, Mr McIntyre said.
The ASX wrote to Oceana Gold on Friday, noting the rise in the share price from A88c on May 19 to $A1.17 and the increase in volume of shares traded.
The company said it was not aware of any information that had not been announced which could explain the recent trading.
The company released its first-quarter results on April 30.
In that release, it confirmed its full-year production guidance of 280,000 ounces to 300,000 ounces of gold at a forecast cash cost of $US365 an ounce to $US405 an ounce.
"Notwithstanding this guidance, movements in gold prices and foreign exchange rates can materially impact on the company's financial results in any given period.
Accordingly, it is difficult to provide earnings guidance for the financial half-year ended June 30, 2009, with a degree of certainty prior to the completion of such period."
Company secretary Matthew Salthouse said the company was a significant Pacific Rim gold producer with three operating mines in New Zealand.
Company guidance confirmed that 2009 was expected to be a year of record gold production across operations.
"The recent increase in the price of gold to its highest level in more than two months, and the strong performance of many of our peer gold producers, may have also increased investor interest in the company."
