Mel Greig and Michael Christian phoned the King Edward VII's Hospital pretending to be members of the Royal Family asking about the duchess's treatment for severe morning sickness.
46-year-old Jacintha Saldanha was found dead three days after taking the call.
The CPS said there was no evidence to support a charge of manslaughter, BBC reported.
Although it said that there was some evidence to warrant further investigation of offences under the Data Protection Act, the Malicious Communications Act 1988 and the Communications Act 2003, it added that this would not take place as any potential prosecution would not be in the public interest.
Malcolm McHaffie, deputy head of special crime at the CPS, said a number of issues had been taken into account in reaching its conclusion.
"It is not possible to extradite individuals from Australia in respect of the potential offences in question. However misguided, the telephone call was intended as a harmless prank," he said.
"The consequences in this case were very sad. We send our sincere condolences to Jacintha Saldanha's family."
Last December, the pair, posing as the Queen and Prince of Wales, tricked Saldanha into transferring the call to a colleague who then described Catherine's condition in detail.
Saldanha was found hanged in nurses accommodation close to the hospital, after apparently taking her own life.
The duchess had been admitted to hospital suffering from hyperemesis gravidarum, acute morning sickness.
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