Vitol's president and chief executive, Scot Ian Taylor, was at the centre of controversy last year when he emerged as a £500,000 donor to the Better Together campaign.
Mr Taylor is said to be very proud of his Scots family roots but was raised and educated in England.
Vitol was founded in Rotterdam, but is headquartered in Switzerland. It has been linked to dubious deals in Serbia, Iraq, Iran and Libya.
The sale of Shell's downstream businesses includes its Geelong refinery near Melbourne and its 870 retail outlets, the Hague, Netherlands-based company said in a statement. It does not include Shell's aviation unit.
"Australia remains important to Shell, but we are making tough portfolio choices to improve the company's overall competitiveness," Shell's chief executive Ben van Beurden said.
Most affected employees will be able to keep their jobs and continue working under Vitol, Shell said.
The deal is subject to regulatory approvals and is expected to be finalised later this year.
Shell has recently sold refineries in the UK, Germany, France, Norway and the Czech Republic.