Rolls-Royce will pay £497.3 million ($617 million, 576 million euros) plus interest to the SFO over a period lasting up to five years.
The settlement approved by Judge Brian Leveson came five years after Britain's Serious Fraud Office began investigating "allegations of malpractice" involving intermediaries in China and Indonesia.
The probe revealed "the most serious breaches of the criminal law in the areas of bribery and corruption", Leveson said in a written judgement issued at Southwark Crown Court in central London.
Under the deal approved on Tuesday Rolls-Royce will pay £497.3 million ($617 million, 576 million euros) plus interest to the SFO over a period lasting up to five years.
The company has also reached separate deal with the United States, under which it will pay the US Department of Justice $170 million.
A settlement with Brazil will see the British manufacturer make payments to the country's Federal Prosecution Service totalling $25.6 million.
Following the settlements being reached, Rolls-Royce Chief executive Warren East apologised for the conduct uncovered during the investigations launched in 2012.
"The behaviour uncovered in the course of the investigations by the Serious Fraud Office and other authorities is completely unacceptable and we apologise unreservedly for it," he said in a statement.
"This was unworthy of everything which Rolls-Royce stands for, and that our people, customers, investors and partners rightly expect from us."
The company said it no longer uses any of the intermediaries implicated in the probe, while a number of people had left the firm as a result of disciplinary action.
The UK probe into Rolls-Royce cost £13 million and was the largest single investigation carried out by the authority, SFO Director David Green said.
The settlement results in the suspension of prosecution against Rolls-Royce, although anti-corruption organisation Transparency International UK called for individuals involved to face charges.
"In order to serve as a proper deterrent for companies who think it is acceptable to do business with bribery, those involved with or who sanctioned bribery must be prosecuted individually," said its executive director, Robert Barrington.
The engine maker Rolls-Royce has no connection with Rolls-Royce cars, a marque owned by the Germany auto maker BMW.