BHP's share of the capital costs is $2.9 billion for its 85% stake, with ITOCHU Minerals and Energy of Australia and Mitsui Iron Ore Corporation holding the balance.
Overall capital intensity is $45 per tonne.
The approval comes after the partners approved an initial $216 million in funding last year for early works.
The 80 million tonne per annum South Flank development is needed to replace BHP's Yandi operation, which is expected to be exhausted over the next five to 10 years.
South Flank is about 100km northwest of Newman and adjacent to BHP's Mining Area C operations, allowing the company to leverage off existing infrastructure.
"South Flank is a capital efficient project which offers attractive returns, and which was approved following a thorough evaluation under BHP's capital allocation framework," BHP president operations, Minerals Australia Mike Henry said.
"The project will create around 2500 construction jobs, more than 600 ongoing operational roles and generate many opportunities for Western Australian suppliers. It will enhance the average quality of BHP's Western Australia Iron Ore production and will allow us to benefit from price premiums for higher-quality lump and fines products."
The development will comprise the construction of an 80Mtpa crushing and screening plant, an overland conveyor system, stockyard and train loading facilities, procurement of new mining fleet and substantial mine development and pre-strip work.
First ore from South Flank is targeted in the 2021 calendar year, with the project expected to produce ore for more than 25 years.
South Flank comprises three deposits - Grand Central, Vista Oriental and Highway - and was a major contributor to a more than doubling of BHP group Marra Mamba reserves to 1.68 billion tonnes at 61.7% iron.
The project will contribute to an increase in WAIO's average iron grade from 61% to 62%, and the overall proportion of lump from 25% to around 35%.
"This is timely given the current dynamics in the iron ore market, with higher-quality products attracting premiums to benchmark prices," RBC Capital Markets analyst Paul Hissey said.
"To this end, the project should help support margins (60% EBITDA margin through 1H FY18) from BHP's Pilbara operations."
CIMIC Group subsidiary CPB Contractors has been awarded the A$260 million infrastructure works contract for the project.
CPB will deliver the construction of bulk earthworks, concrete and underground services, starting next month and running until September 2020.
"The South Flank development works will help to ensure that the Mining Area C precinct becomes one of the largest standalone iron ore processing centres in the world, and it is our privilege to again be working with BHP to deliver high-quality assets of long-term value," CIMIC CEO Michael Wright said.
Premier Mark McGowan today welcomed the announcement by BHP and its joint venture partners to develop the South Flank mine in the Pilbara, a project that will create more than 3,000 Western Australian jobs.
WA Premier Mark McGowan welcomed the announcement and the jobs it would create for the state.
"The investment is welcome news for Western Australia, and yet another sign that the economy is turning the corner and jobs are being created for Western Australians," he said.