Shell sold a third of its Woodside holding in 2010, reducing that 34% stake to the 23.1% it holds now.
Woodside has recommended shareholders vote in favour of the buy-back, which chief executive Peter Coleman said would deliver value.
“This combined transaction is an efficient and disciplined use of capital and creates value for all our shareholders,” Coleman said.
“In parallel, it allows us to optimise the company’s near-term capital structure, while maintaining the capacity to continue to develop existing projects and make additional investments in new growth opportunities.
“The combined transaction will also increase our liquidity in the market and resolve the uncertainty in relation to Shell’s shareholding that has existed for several years.”
The company added this was not expected to impact the company’s credit rating and would preserve Woodside’s growth plan.