The firm said it had given the Serious Fraud Office (SFO) information about allegations of malpractice in Indonesia and China, and has identified “matters of concern” in these and other countries.
The allegations, which have not been revealed, came to light after the SFO asked Rolls-Royce to conduct an internal probe.
“It is too early to predict the outcomes, but these could include the prosecution of individuals and of the company. We will cooperate fully,” said chief executive John Rishton.
“I want to make it crystal clear that neither I nor the board will tolerate improper business conduct of any sort and will take all necessary action to ensure compliance.”
A source close to the investigation said the allegations relate to events in the “distant past”, suggesting the events would not be covered by the Bribery Act, which came into force in 2011. The US Department of Justice has also been informed of the probe.
The SFO has taken a tougher stance on firms self-reporting possible corruption since David Green took over as director in April.
“The announcement that Rolls-Royce has disclosed this morning… may just turn out to be the Christmas present that David Green has been waiting all year for,” said James Carlton, a partner at law firm Fox Williams.
Shares in Rolls-Royce fell 3.1 per cent to 885p yesterday, wiping more than £500m from its market value.