Gold Coast man Agim Ajazi, 30, briefly appeared in Brisbane Magistrates Court on Tuesday after arriving in South Australia on Sunday.

He is accused of supporting terrorist organisation Jabhat al-Nusra in Syria between 2014 and 2016.

The five commonwealth terror offences Ajazi is charged with are: incursion into a foreign state with the intention of engaging in hostile activity, engaging in hostile activities in a foreign country, membership of a terrorist organisation, providing support to a terrorist organisation and advocating terrorism.

Australian authorities began investigating Ajazi in 2013 before he left Australia and continued to monitor him in Syria.

Court documents allege he arrived in Syria on March 1, 2014, and became a member of the terrorist group.

Ajazi is also accused of spreading propaganda and performing guard duties from July 1, 2014, to September 30, 2016.

"This group adheres to violent extremist ideology and maintains links to Al-Qaeda," Australian Federal Police Assistant Commissioner Counter Terrorism Ian McCartney told reporters.

While in Syria, Ajazi allegedly fought under the nom de guerre Ahmed Shaheed and used social media to document his activities.

Information collected from his accounts will form a significant part of the Commonwealth's evidence against him, Mr McCartney said.

"He's recorded as boasting about the killing of non-Muslims in a conflict zone," he said.

Ajazi also made references to attacking non-Muslims in the West, including Australia, the US and UK.

"This (was) not about religion, this (was) about criminality and violent extremism," Mr McCartney said.

Ajazi was taken into police custody on his arrival in Adelaide on Sunday before being extradited to Brisbane on Monday.

He was not required to enter a plea in court and was remanded in custody until his next court date on January 10.

Australian Associated Press