Australia, which until Sunday had gone two weeks without any locally acquired cases of Covid-19, is expected to begin administering vaccines this month.
Australia's Covid-19 inoculation programme will cost at least $4.8 billion.
Although it has pledged to spend $3.3 billion to acquire enough doses for its 26 million population, Morrison will say that his government has set aside a further $1.4 billion to pay for the roll-out.
"The strategy is backed by an initial allocation of around $1.4 billion in new support for the vaccine roll-out. This is on top of more than $3.3 billion allocated for vaccines purchases," according to extracts of a speech Morrison will deliver in Canberra on Monday.
Classifying the inoculation programme as his "first priority," Morrison will add that the country's economy must now begin to wean itself from government spending.
Australia has pledged more than $191 billion in stimulus, which has already begun to taper.
Highlighting recent strong economic data, Morrison will say there is a limit to the support government can afford.
“We are not running a blank cheque budget," Morrison will say in the speech.
Morrison's speech comes as the Australian city of Perth begins its first full day of lockdown after the detection of a Covid-19 case.
The person infected, a security guard in his 20s, was working at a hotel where four people in quarantine had active cases of the virus, including the highly contagious strains that have been linked to Britain and South Africa, local health authorities said.
Calls for pharmacists
Australia will invite pharmacies this week to join the government-funded rollout of Covid-19 vaccine, the federal government said.
The government will ask the country's roughly 5,800 community pharmacies to apply for the program, which would pay them to administer inoculations, along with doctors and hospital health workers.
"That means more points of presence for Australians in terms of where they can receive their Covid-19 vaccine," Health Minister Greg Hunt told reporters.
"This is potentially life-saving medication. The medicines can work with differing degrees of effectiveness, but all up, this can improve lives, extend lives, or save lives."
The government plans to start vaccinating priority groups like older and Indigenous Australians with a shot developed by Pfizer Inc and BioNTech SE from late February.
The plan also involves a vaccine developed by AstraZeneca Plc, although that product has not yet been approved by Australia's Therapeutic Goods Administration. Pharmacists involved in the program would receive training to administer the AstraZeneca vaccine, with first shots planned in May, Hunt said.