Mr Donnelly said the reason the portal has been opened for younger people sooner than expected is because the vaccination programme is ahead of schedule.
A PPS number, Eircode, email address and phone number are all needed for registration on the HSE portal.
The mRNA vaccines are Pfizer and Moderna. Both vaccines require two doses which are given four weeks apart.
Currently, those aged between 18 and 34 can continue to receive the single-shot Janssen vaccine in pharmacies.
Mr Donnelly wrote on Twitter: “All those 18+ can register for an mRNA vaccine (Pfizer / Moderna) from tomorrow.
“This is because our vaccination programme is ahead of schedule and continues to perform really well.
“Huge thanks to our vaccination teams and volunteers in vaccination centres.”
As of the latest figures released yesterday, 5,230,100 vaccine doses have been administered in Ireland.
More than 70pc of the adult population has now had at least one dose of the vaccine, and almost 60pc of adults are now fully vaccinated.
This comes as 1,110 more Covid-19 cases were confirmed by the Department of Health today.
However, hospitalisations have dropped as there are now 89 patients with the coronavirus in hospital, 21 of whom are in ICU.
This is 12 fewer coronavirus patients in hospital than was reported yesterday.
Over the past week there has been an increase in cases of 88pc compared to the week before.
Incidence rates have increased in every county over the past seven days. The counties with the highest 14-day incidence rates are Donegal with 725 per 100,000 population, Louth with 474 per 100,000 population, Dublin with 307 per 100,000 population, Limerick with 258 per 100,000 population and Galway with 257 per 100,000.