The $2.6 billion deal, announced Friday, also includes Shell's bulk fuels, bitumen, chemicals and part of its lubricants businesses in Australia.
Shell's announcement comes amid a $15 billion divestment program to be carried out over the next two years, overseen by Ben van Beurden, who took over as chief executive officer in January.
"Australia remains important to Shell, but we are making tough portfolio choices to improve the company's overall competitiveness," van Beurden said in a news release.
Citing Australia's growing economy, Vitol chief executive Ian Taylor said the company, based in Rotterdam, Netherlands, is aiming to build a presence in Australia, the Sydney Morning Herald reported.
''We are buying the business to build the business,'' Taylor was quoted as saying by the Herald.
''There's a lot of developments going on in Australia with resources, with the LNG projects, and we want to make sure we are supplying all the fuel that is required for the new mining projects," Taylor said. "That is the sort of thing we will be chasing hard."
As for the 55-year-old Geelong refinery, Taylor said Vitol needs to spend "quite a bit of money'' on maintenance at the facility, but he said it could be run profitably by improving logistics and doing some hedging on currencies.
''We think there probably will need to be more [fuel import] terminals in the longer term. ... It's on that side of the terminal and distribution business that we will probably be looking for the most opportunities," Taylor said.
The Shell-Vitol deal is subject to regulatory approvals, and is expected to close this year, Shell said.
Experts predict Australia could soon overtake Indonesia as the biggest importer of refined oil products, the Financial Times reported, citing the closure of old and high-cost refineries in the country and rising demand from its mining sector.
A report released Monday by Australia's National Roads and Motorists' Association, known as the NRMA, warns Australia's reliance on imported fuel leaves the country's transport network vulnerable to a global oil supply crunch.
The NRMA estimates Australia now imports about 90 percent of its crude oil and refined petrol. That compares with 60 percent 14 years ago.