ASC Shipbuilding, now wholly owned by the Commonwealth, will become a subsidiary of BAE Systems.
"This deal is a flawless illustration that the Government is doing exactly that. and it will also cement our strategic partnership with one of our oldest and closest friends for decades to come".
"Fantastic news that #Australia has chosen @BAESystemsplc Type 26 frigate..."
The vessels will replace Australia's current nine ANZAC class frigates, with the new ships equipped with a long-range cutting-edge missile defence system to counter threats from rogue states like North Korea.
Meant to begin replacing the eight workhorse Anzac-class frigates of the Royal Australian Navy (RAN) in 2027-28, the new Hunter class will be constructed by ASC Shipbuilding at Osborne on the outskirts of Adelaide.
Britain said the Â£20-billion deal was "a result of four years of intensive government engagement", and hailed it as a boost for its post-Brexit prospects.
BAE Systems Chief Executive, Charles Woodburn, said the decision "reinforces our position as a leading designer and builder of complex maritime platforms".
With the announcement, the organisation has awarded BAE Systems a US$198m contract for the low rate production of 30 Amphibious Combat Vehicles, with initial options for a total of 204 vehicles which, if exercised, could take the deal value up to US$1.2bn.
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Regarding shipbuilding arrangements, Turnbull noted: 'The next generation of frigates will be built by ASC Shipbuilding at the Osborne Naval Shipyard.
While the overall budget is £20bn (35bn Australian dollars), only a part of that will come to BAE Systems for the design and build of the frigates.
The dubbed Hunter class warships will be developed in Adelaide, creating 4,000 jobs in Australia, the Turnbull government announced.
A Defence source told the newspaper the vessels will be the most advanced of its type specialising in anti-submarine warfare, saying: "They kill submarines".
At the end of the program the Commonwealth will resume complete ownership of ASC Shipbuilding, thereby ensuring the retention in Australia of intellectual property, a highly skilled workforce and the associated equipment.
The frigates will have enough range to operate throughout the region and the ability to support non-warfare roles including humanitarian assistance and disaster relief, it said.
BAE Systems, which won the lucrative SEA 5000 project with its high-tech "Type 26" frigate offering, was competing against Fincantieri of Italy with its FREMM, and Navantia of Spain with an updated F100.