The business, Earnd, is the Sydney division of the Covent Garden-based Earnd group which pays NHS staff their wages before payday.
It is being bought by a rival company called Wagestream, the specialist website Sifted reported.
However, the sale, likely to have been in the low single millions of Australian dollars, will make barely a scratch on the £1 billion it owes creditors like Softbank and Credit Suisse.
Greensill’s collapse sparked concerns that Earnd’s service to cash-strapped nurses would be scrapped, as the Evening Standard reported last week.
Wagestream provides a similar service to Earnd but charges the employees, whereas Earnd levies the fee on the company.
JD Sports is among the Australian clients of Earnd.
Wagestream chief executive Peter Briffett told Sifted: “It happened very quickly… we got in touch with administrators… We were really interested.”
Earnd is the market leader in Australia and Briffett said it was a “perfect fit” for Wagestream.
The biggest creditor of Greensill is