The immunisation drive is expected to begin in the spring, Roberto Speranza said in an address to parliament.
Italy will get its vaccines via an EU procurement programme and is waiting for the European Medicines Agency's green light.
Britain on Wednesday became the first western country to approve a Covid-19 vaccine for general use, announcing the rollout of a vaccine developed by Germany's BioNTech and its US partner Pfizer from next week.
Meanwhile Europe's medicines regulator has said it will decide by December 29 whether to grant emergency approval to Pfizer-BioNTech's jab, ahead of another potential treatment from Moderna.
The latest timeline suggests Europeans could receive the first jabs before the year is over.
Nonetheless, Speranza said: “We can finally see light at the end of the tunnel.”
The health minister said Italy has signed contracts for vaccines from AstraZeneca, Johnson & Johnson, Sanofi, Pfizer, CureVac and Moderna.
Who will be first to get the vaccine?
Once approval comes, doctors and health care workers will get the first doses – some 1.4 million people.
They will be followed by residents in care homes – just over 570,000 people.
Those aged over 80 will be next in line, followed by those aged 60-79, and those suffering from at least one chronic disease.
Vaccines will then be distributed to key workers — teachers, police, prison wardens
After that, it will be offered to the general population at walk-in centres.
“It will not be obligatory at first. The government will be monitoring how the campaign progresses,” he added.
“The vaccine will be distributed to all Italians for free,” Speranza said.
This is unlikely to mean however that the vaccine would be available only to Italian citizens.
All current mandatory or recommended vaccines are available to everyone in the country – including those not registered with the SSN (National Health Service).
Speranza also said people in Italy should prepare for restrictions to continue over the Christmas holidays – though he did not give concrete details of new measures due to come into force when the previous restrictions expire this week.
“I warn you now: do not mistake the first ray of sunlight for an escape from danger,” he said, adding: “If we let down our guard now, the third wave is just around the corner.”
Speranza urged all lawmakers in Italy, where campaigners against vaccination are very vocal, to get behind the immunisation push.
“There's no government majority or opposition on this, there are simply Italians,” he said.
One recent survey found that nearly 50 percent of people asked in Italy said they would have doubts about getting vaccinated, including 11 percent who described themselves as “completely against” a vaccine.
Scientists estimate that 60-90 percent of a population needs to be vaccinated – possibly every year – to reach herd immunity against the coronavirus and stop future outbreaks.