As well, Justice Minister Michael Keenan will become minister assisting the prime minister on counter terrorism.
Foreign Minister Julie Bishop told ABC radio on Monday the appointments would ensure "nothing slips through the cracks" in the fight against terrorism.
Regarded an authority on security and intelligence, Mr Moriarty will head a new counter-terrorism co-ordination office within Mr Abbot's own department.
A former ambassador to both Tehran and Jakarta, he has extensive knowledge of Islam and its radical variants and has experience as an inter-agency operator.
New counter-terrorism laws to go to parliament
Parliament is expected to consider counter-terrorism laws to extend the government's power to strip citizenship from people who fight against Australia.
Prime Minister Tony Abbott indicated at the weekend the new powers would be put to the lower house in the coming week.
It would extend an existing power that allows the government to take citizenship away from people who fight with foreign armies against Australia.
The measure could lead to second-generation Australians who join extremist organisations losing their status if they are also citizens of their parents' birth country.
Opposition Leader Bill Shorten has sought a briefing on the new laws before deciding whether Labor will offer its support.
