The sale covers Shell's Geelong Refinery and 870-site retail business, along with its bulk fuels, bitumen, chemicals and part of its lubricants business in Australia.
It also includes a brand licence arrangement and an exclusive distributor arrangement in Australia for Shell Lubricants.
The aviation business will remain with Shell Group. So too will the lube oil blending and grease plants in Brisbane, which will be turned into bulk storage and distribution facilities.
The decision does not affect Shell's upstream business.
The deal is part of a range of divestments Shell CEO Ben van Beurden foreshadowed earlier this year.
"Australia remains important to Shell but we are making tough portfolio choices to improve the company's overall competitiveness," he said.
Shell Australia country chair Andrew Smith said the company had been involved with Australia for 113 years.
"Like any business that operates for over a century, Shell's business has changed over the years and we are pleased to have found a buyer for the Geelong refinery," he said.
The deal is subject to regulatory approvals and is expected to close this year.
Shell also announced that it, and Kuwait Petroleum International, had reached an agreement to sell shares in the companies containing the retail, supply and distribution, and logistics and aviation business in Italy.
Under the agreement Shell's retail network will be rebranded Q8.
It did not disclose a price for the sale.
Other downstream divestments by Shell include the sale of refineries in the UK, Germany, France, Norway and the Czech Republic, plus downstream businesses in Egypt, Spain, Greece, Finland and Sweden.
Shell also has created a joint venture with Vitol and other partners across Africa.