Theresa May says the deal puts the UK at the “very forefront of maritime design and engineering”.
Shares in BAE rose by more than 1% following the announcement.
The frigates will be built down under but the PM said the export of a British design was an “enormous boost” for the UK economy.
The prime minister raised the possible deal with Australian PM Malcolm Turnbull at Chequers earlier this year, and its award follows four years of high-level talks between the two countries.
It is part of a £112bn spending programme by the government in Canberra.
Among the firms competing with BAE were Spain’s Navantia and Italian firm Fincantieri.
BAE Systems chief executive Charles Woodburn said the contract reinforced the company’s position as a “leading designer and builder of complex maritime platforms”.
“I am proud that our world-class anti-submarine warfare design and our approach to transferring technology and skills to the nations in which we work is expected to contribute to the development of an enduring world-class naval shipbuilding industry in Australia,” he said.
Mrs May said: “The sheer scale and nature of this contract puts the UK at the very forefront of maritime design and engineering, and demonstrates what can be achieved by UK industry and Government working hand-in-hand.
“We have always been clear that as we leave the EU we have an opportunity to build on our close relationships with allies like Australia. This deal is a perfect illustration that the Government is doing exactly that.
“While this is an enormous boost for the UK economy, it will also cement our strategic partnership with one of our oldest and closest friends for decades to come.”
BAE Systems is on a roll after winning a £150m tank contract with the US Marine Corps last week.