The remaining sites in Sydney, Parramatta, Brisbane, Perth and Adelaide have been purchased by Hallmark Group, the publication reports.
Aramark's president in Northern Europe, Frank Gleeson, commented, "We are passionate about the health and well-being of those we serve every day, so it was a natural fit for us to partner with Jamie Oliver".
The Australian arm of the restaurant group has been put into administration in order to change ownership of the chain, the company said.
Mr Oliver's Australian company, set up in March previous year to buy the restaurants from their failed owners, went into voluntary administration yesterday.
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In a statement via social media the Canberra restaurant said: "This is pretty sad news for the staff but Jamie's Italian has closed suddenly this morning and it looks like it won't be reopening anytime soon".
Jamie Oliver's business woes have deepened with his Australian restaurant group falling into voluntary administration. The St Paul's branch of the steak restaurant was saved in a pre-pack deal whereby a different subsidiary of Oliver's restaurant company bought the site.
They also announced that Brisbane-based Hallmark Group would take over operating the Australian franchise of the Italian chain.
Oliver's businesses are not only struggling to make ends meet overseas. "We have got a great business, and we will bounce back".