Prakash, a senior recruiter for so-called Islamic State, was arrested in Turkey last year and placed in jail.
Earlier last year, Australia incorrectly announced that Prakash - who has been linked to foiled terror attacks - had died in a US air strike.
The Melbourne-born man will now face trial in Australia, Mr Turnbull said.
"We have an extradition treaty with Turkey," Mr Turnbull said on the local Seven Network on Friday.
