The Minister for Health says the first mass vaccination centre for COVID-19 shows that there "is light at the end of the tunnel".
Around 1,000 people over the age of 85 are receiving their first dose of the vaccine at a GP hub in DCU today.
Other centres in Cork and Galway will be up and running in the coming weeks.
The HSE says just under a fifth of over-85s will have had their first dose by tomorrow.
Speaking from DCU, Minister Stephen Donnelly said it is a hugely positive development.
"It's been the most brutal, hard year for people with so much loss, so much suffering, and to see this today, this is the light at the end of the tunnel," he said.
"Everyone who's been vaccinated here today will get their second dose in 28 days' time.
"Just talking to people here, talking about their hopes and how they're going to start getting on with their lives again is just wonderful."
Minister Donnelly added that Ireland has one of the fastest rollouts of coronavirus vaccines in the EU.
So far, over 310,000 doses have been administered with just under 200,000 people receiving their first dose.
The Health Minister said we are on course to administer a million doses a month from April when more supply becomes available.
"Ireland has one of the fastest vaccine rollouts in the EU," he said.
"People are very reasonably looking at the UK and saying they're ahead, and they are, we have to accept that.
"We are a member of the EU, we're going with the EU, and had we gone on our own, and as a tiny country tried to purchase millions and millions of doses of vaccine, it's not at all certain that we would have been able to do that, we would have been competing with the might of the EU."
Positivity and joy were the two things I heard from people aged 85 and over today getting their vaccines at the GP hub in @DCU Almost 1000 getting their vaccines today. Our GPs, nurses and support teams are making this happen with @HSELive pic.twitter.com/nUoHVxbudP
— Stephen Donnelly (@DonnellyStephen) February 20, 2021
Meanwhile, the CEO of the HSE Paul Reid described the scenes in DCU today as "uplifting, inspiring and quite emotional".
"So many 85-plus-year-olds and their families expressing gratitude and joy as they received their vaccination in The Helix at DCU. Days like this give us all confidence and hope for 2021."
He said the HSE is ramping out the rollout of the coronavirus immunisation to over-85s.
"We started the vaccination programme just this week for the 85-year-olds plus, by the end of this week we will have vaccinated about 13,500 over-85s," he explained from the Helix.
"There's a total population of that age of around 72,000 and they will all have received their first vaccination between this week and the next two weeks."
It comes as three cases of the Brazilian COVID-19 variant have been found in Ireland for the first time.
The Deputy Chief Medical Officer Dr Ronan Glynn said further studies are needed to determine whether this variant is likely to have an impact on vaccine effectiveness or infection severity.