CSL said it expects to supply 30 million doses of a vaccine being developed by AstraZeneca AZN.L and Oxford University to the Australian government if trials prove successful, with the first doses to be available in early 2021.
The Greek government has said that any Covid-19 vaccine would not be compulsory but it will be "strongly recommended".
Australia in August said it would buy the AstraZeneca vaccine, but the deal appeared in some doubt in August after CSL said it was prioritising its own rival vaccine.
J&J's vaccine is one of over a hundred worldwide being developed in response to the coronavirus pandemic, which has infected almost 26.5 million people and led to some 869,323 deaths.More news: Fortnite-gate: Google Will Attempt to Have Epic's Antitrust Lawsuit Dismissed
The trials are expected to begin in the coming week, following ethics committee approvals, said sources close to the development.
If the trials are successful, Mr Morrison says Australia will have early access to 3.8 million doses in January and February 2021 for vulnerable people and frontline health workers.
Australians will only need to take one of the successful vaccine candidates, with an initial dose followed by a booster dose of the same vaccine within weeks.
J&J comes as multiple companies near the ends of the final stages of clinical trials for the prospective vaccines and the increasing concerns of vaccine nationalism from agencies like the World Health Organization (WHO).More news: Australia secures onshore manufacturing agreements for two COVID-19 vaccines
In addition, it is looking to participate in phase 3 trials with French drugmaker Sanofi, Johnson & Johnson's Janssen unit and Chinese companies CanSino Biologics Inc and Walvax Biotechnology Co Ltd, all of which have agreed to guarantee access to their vaccines if successful. "Now more than ever Australians are aware of the importance of investment in research".
The federal government has nailed down two possible vaccine sources with supply and production agreements with pharmaceutical companies worth $1.7 billion.
First doses of that vaccine are scheduled for release in early 2021, depending on the results of the latest human trials.
Prime Minister Scott Morrison said at the time it was "one of the most promising and most advanced vaccine developments anywhere in the world". CSL's CEO and Managing Director Paul Perreault said, "We are pleased that we can produce the AZD11222 without compromising the production of our core products - influenza vaccines and plasma and recombinant protein therapies - and provide a second option for a COVID-19 vaccine candidate to Australia".More news: US Veterans Issue Open Letter in Support of Trump