The Australian Maritime Safety Authority confirmed a 60-year-old man and a 48-year-old woman who were on board the 19-metre yacht were rescued about 7.25am on Tuesday.
The pair are believed to be uninjured, but the boat - the Spirit of Mateship - had to be abandoned.
AMSA said it received a distress beacon alert about midday on Monday, but choppy conditions due to strong winds plagued rescue efforts.
A mechanical failure led to the yacht becoming stranded around 185km east of Nowra, but it drifted further east to sit around 300km offshore before the duo were saved.
Navy vessel HMAS Canberra assisted in the rescue effort, as did NSW Police vessel Nemesis.
HMAS Canberra's captain Brendan O'Hara said the duo's near-24-hour ordeal would have been torturous, given his far-more-sizeable ship had also battled the powerful swells.
Winds of between 50 and 70km/h along with seas of up to 6m had made executing the rescue effort challenging for crews, conditions Capt O'Hara labelled "quite extreme".
"(The pair) were just holding on as best they could … I hate to think what it was like for them, because even on board Canberra, which is quite a large ship, we were rocking and rolling a fair bit," he told Seven's Sunrise program.
"Not much of the crew here have had much sleep, so the two personnel in Spirit of Mateship definitely had no sleep at all, I dread to think about the conditions in there."
AMSA duty manager Ben Flight said the rescued pair were believed to be in good shape considering the ordeal.
"We've safely recovered the two people on board the police vessel Nemesis … we understand, all things considered, they're in good conditions," he told Sydney radio 2GB.
"The police vessel Nemesis and the HMAS Canberra are both heading back towards the coast and we understand they're going to go back to Sydney tonight to take the two people off."
HMAS Canberra arrived on scene at 1am on Tuesday, while the police boat got there at 3am.
The duo will be taken back to Sydney for medical assessment.
The choppy conditions initially prevented authorities from winching the duo out of their boat and airlifting them to medical facilities.
Earlier on Tuesday, AMSA officials said the matter had become "time-sensitive" with the boat taking on water.
Two Royal Australian Navy ships and an RAAF C-130J Hercules aircraft were initially involved in the rescue operation.
The Spirit of Mateship has entered a number of Sydney to Hobart races, crewed by wounded and injured former defence force personnel to raise money for charity Mates4Mates.
Former prime minister Tony Abbott launched the boat in 2013 before the vessel's first Sydney to Hobart effort.
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