The SBS devoted four minutes on its radio channel to the visit and published a story on its website to highlight the signing of the bilateral strategic partnership.
The ABC group and the The Courier weekly also ran similar stories and photos on the welcome ceremony, talks and signing of documents of the two Prime Ministers.
The articles noted that Vietnam and Australia have officially ramped up diplomatic ties ahead of a special summit of South East Asian leaders, with the two PMs signing a bilateral strategic partnership aimed at deepening defence, security, trade, investment, development and tourism links on March 15.
"This announcement is a fitting way to mark 45 years of diplomatic relations," the articles quote PM Turnbull as saying.
The local press also reported on the signing of separate deals on education and research.
They stressed that Vietnam and Australia last week signed up on to the Trans-Pacific Partnership free trade pact, adding that Vietnam is the fastest-growing economy in ASEAN.
The Australian press noted that PM Phuc is the first Southeast Asian leader to arrive ahead of the Australian-ASEAN special summit in Sydney, which kicks off on March 16.