He also expects the AstraZeneca vaccine will finally get the nod of approval from the Therapeutic Goods Administration within the next few days.
"Australia is on track for our vaccine rollout," Mr Hunt told reporters in Canberra on Sunday.
Border workers, those in aged care and their carers will be among the first to get the vaccine.
Deputy Prime Minister Michael McCormack said Australia will receive 20 million Pfizer doses in 2021.
He has been assured that DHL's ultra-cold and secure storage facility can safely manage the vaccine, which needs to be stored between minus 60 and 80 degrees.
Mr McCormack said DHL is one of two world-class logistics and distribution companies contracted to ensure the COVID-19 vaccines are available to everyone in Australia, no matter where they live.
"I have been determined to ensure that regional and rural Australia gets the same access to the vaccine that our cities will and that's what we are doing," Mr McCormack said.
DHL will also distribute the Astra Zeneca and Novavax vaccines – when approved – to Victoria, Tasmania, South Australia, the Northern Territory, Western Australia and external territories, such as Norfolk Island.
AUSTRALIA'S PHASED VACCINE ROLLOUT
Phase 1a (up to 1.4 million doses):
Quarantine and border workers, frontline healthcare workers, aged care and disability care staff, aged care and disability care residents.
Phase 1b (up to 14.8 million doses):
Elderly adults aged 80 years and over, elderly adults aged 70-79 years, other healthcare workers, Aboriginal and Torres Strait Islander people aged over 55, younger adults with an underlying medical condition, including those with a disability, critical and high-risk workers including defence, police, fire, emergency services and meat processing personnel.
Phase 2a (up to 15.8 million doses):
Adults aged 60-69 years, adults aged 50-59 years, Aboriginal and Torres Strait Islander people 18-54, other critical and high-risk workers
Phase 2b (up to 16 million doses):
Balance of adult population, catch up any unvaccinated Australians from previous phases.
Phase 3 (up to 13.6 million doses):
If recommended for people under 16 years.