Nurse Jacintha Saldanha (46) put their call through to Kate's ward at the King Edward VII Hospital in London, where an unnamed colleague gave details of the duchess's treatment for severe morning sickness.
A recording of the conversation was broadcast on the 2Day FM station, with the DJs gleefully boasting about their successful hoax.
Mrs Saldanha apparently took her own life after last week's incident.
"There's not a minute that goes by where we don't think about her family and what they must be going through and the thought we may have played a part in that is gut-wrenching," Ms Greig said.
The pair wept at times during the TV interview -- their first public appearance since Mrs Saldanha's death -- revealing the "simple harmless phone call" had been the joint idea of their production team.
"It was just the team sitting down before the show ... we just had the idea for just a simple harmless phone call.
"That we thought about making a call, it was going to go for 30 seconds, we were going to be hung up on and that was it. As innocent as that," host Michael Christian said.
Former model Mel Greig claimed they had believed other media organisations would also have tried the 'gag' and they couldn't believe it when the call was patched through to the nurse on duty.
"We thought a hundred people before us would've tried it, we thought it was such a silly idea and the accents were terrible and not for a second did we expect to speak to Kate, let alone have a conversation with anyone at the hospital. We wanted to be hung up on."
The young DJ described learning the news that Mrs Saldanha had died as "the worst phone call I've ever had in my life".
Breaking down in tears, Ms Greig added: "These prank calls are made every day, on every radio station, in every country around the world and they have been for a long time. No one could've imagined this to happen."
The controversy surrounding the prank call has so far shown no signs of abating. At the weekend, the chairman of King Edward VII Hospital, penned a letter to the radio station, condemning the prank call.
In response radio station bosses have said they are reviewing its broadcasting practices and will help with investigations. Scotland Yard has already contacted police in Sydney and it is understood they may wish to interview the two DJs.