The man, 43, was arrested at his Melbourne home on Tuesday after a 16-month investigation by counter-terrorism authorities.
There is no current threat to the public, authorities said.
Police allege the Australian national helped run a promotional website for the US man and sent about A$5,000 (£3,000; $4000) to him in Syria.
The money was allegedly transferred in up to 10 transactions between April 2013 and November 2014.
They included the suspect's own money and payments he had received from unidentified bank accounts overseas, police said.
