The girls, who were born six weeks early by emergency caesarean, were with their parents -- Renee Young and Simon Howie -- when they passed away, the Nine television network reported.
"It is with great sadness that we share this news with you," said the broadcaster, which has had access to the parents before and after the birth.
Westmead Children's Hospital in Sydney's west, where the sisters were undergoing treatment after their birth in early May, confirmed the deaths but said Young and Howie were not releasing further information.
Howie told Woman's Day magazine in an earlier interview that the "little Aussie fighters" had started developing their own personalities.
"Faith tends to cry a little more, while Hope takes after her mum and likes to sleep a lot," Howie said.
"Faith blows little bubbles and loves sucking her thumb but Hope prefers the dummy."
The couple, who are parents to seven other children, said they could not face terminating their pregnancy despite concerns about the babies' survival.
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