The Crown Prosecution Service (CPS) confirmed that the Metropolitan Police Service had provided the CPS with a file of evidence on December 19, 2012 and sought its advice on the bringing of a prosecution.
Greig and Christian's Hot 30 programme was taken off the air in December following the death of nurse Jacintha Saldanha, who forwarded the show's call to the royal's nurse at London's King Edward VII hospital.
Despite possible breaches of the Data Protection Act 1998, the Malicious Communications Act 1988 and Communications Act 2003, it has been decided that any prosecution would not be in the public interest.
Deputy head of special crime at the CPS Malclolm McHaffie said: "In reaching this decision, the CPS has taken into account the following, among other, matters.
[L: Jacintha Saldanha, R: Duke and Duchess of Cambridge leave King Edward VII Hospital]
"[Firstly] it is not possible to extradite individuals from Australia in respect of the potential offences in question... [Secondly] however misguided, the telephone call was intended as a harmless prank."
He added: "The consequences in this case were very sad. We send our sincere condolences to Jacintha Saldanha's family."
The pair were reportedly moved to safehouses and assigned bodyguards following the incident, and their show was formally cancelled earlier this week.
Greig and Christian later said that they were "gutted and heartbroken" after the death of Saldanha.
Owner of 2Day FM Southern Cross Austereo suspended advertising on the station and banned prank calls across its network.
Later owner Sandy Kaye later called the UK backlash a "witch hunt".
"It's intense and what's incredible to me is it's so much easier for the British media to have us as the target. They haven't once looked at the hospital," he added.
Saldanha's children later said their mother's death left an "unfillable void" in their lives.