Perry Kouroumblis was arrested at Rome's Leonardo Da Vinci Airport in September over the slaying of Suzanne Armstrong, 28, and Susan Bartlett, 27, in January 1977.
The friends were found dead with multiple stab wounds in their home on Easey Street in Collingwood in Melbourne's inner north.
Ms Bartlett's 16-month-old son Gregory was found unharmed in his cot.
Perry Kouroumblis is expected to arrive at Melbourne airport after being arrested by police. (Con Chronis/AAP PHOTOS)
Kouroumblis was pictured by several media outlets being escorted onto a Qatar Airways flight, flanked by a ring of security, which departed on Monday afternoon local time.Â
Footage on board the plane captured by 7News showed the 65-year-old sporting a white beard and grey wavy hair in a black jumper and glasses en route to Melbourne.
He is expected to land on a second flight from Doha at 11.45pm on Tuesday after earlier being transferred into the custody of homicide detectives.
The dual Greek-Australian national previously told Italian authorities he was "happy" to be extradited but a judge will have final sign off.
Charges have not been laid and he maintains his innocence.
Kouroumblis' lawyer, Serena Tucci, said her client was prepared to face trial and his extradition could happen without a court appearance.
"It's very possible that the judge's signature could happen right as the guards are there at the prison, and within an hour, he's gone," she told the ABC last month.
Victoria Police had an INTERPOL red notice alert out for Kouroumblis on two charges of murder and one of rape.
But he was not able to be arrested in Greece due to a 20-year statute of limitation on the initiation of murder charges.
Shane Patton described the murders as an "horrific, frenzied homicide". (Diego Fedele/AAP PHOTOS)
Ms Armstrong and Ms Bartlett were last seen alive on January 10, 1977, and their bodies were found three days later.
Victoria Police Chief Commissioner Shane Patton has described the murders as "an absolutely gruesome, horrific, frenzied homicide".
He said advances in technology, investigative techniques and retracing statements had contributed to the breakthrough.
"This is Victoria's most serious cold case and longest cold case that we have ever solved, and that's why it is such a significant achievement," Mr Patton said.
"There is simply no expiry date on crimes that are as brutal as this".
The force offered a $1 million reward in 2017 to catch those responsible.
The women went to school together at Benalla in Victoria's north and their families said their deaths changed many lives "irrevocably".
The women's families said it was difficult to express their level of appreciation to investigators who tirelessly pursued answers and justice for so long.
"The perseverance and dedication required to achieve the result today is something to truly behold," they said in a statement on Saturday.
"For always giving us hope and never giving up, we simply say, thank you."
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