Mr Turnbull and Mr Phuc signed a new strategic partnership aimed at deepening defence, security, trade, investment, development and tourism links on Thursday.
"This announcement is a fitting way to mark 45 years of diplomatic relations," Mr Turnbull said.
They also inked separate deals on education and research.
Australia and Vietnam are set to increase cooperation on vocational education and training.
Prime Minister Malcolm Turnbull is being urged to put a series of controversial human rights issues on the agenda when he meets with ASEAN leaders in Sydney this weekend.
Human rights campaigners want the prime minister to raise the anti-democratic crackdown in Cambodia, the Rohingya refugee crisis in Myanmar, and restrictions on free speech in Thailand, Vietnam, Malaysia and Singapore during the two-day summit.
