The first results of the UK vaccination programme suggests it is having a "spectacular" impact on preventing serious illness.
Research led by Public Health Scotland found at four weeks after the first dose, hospital admissions were reduced by 85% and 94% for the Pfizer and AstraZeneca jabs respectively.
It is the first sign of the real world impact of vaccination in the UK.
Figures for England are expected to be released later.
Among the over 80s, there was an overall 81% reduction in the numbers admitted to hospital.
The researchers did not look at the impact on transmission - whether people who were vaccinated passed it on - or whether immunity waned over time.
The preliminary data from the EAVE II project covers 1.14 million vaccinations given in Scotland between 8 December and 15 February.
The study looked at the numbers being admitted to hospital with Covid among this population and compared it to those admitted who were not vaccinated.
In total, there were just over 8,000 people who ended up in hospital, but only 58 were among the vaccinated group after the four-week mark.
Lead researcher Prof Aziz Sheikh said the results were "very, very" impressive and both vaccines were working "spectacularly".
"These results are very encouraging and have given us great reasons to be optimistic for the future."
Trials of both vaccines had suggested they would have a significant impact at preventing hospitalisations.
But for the Pfizer vaccine studies, that had involved a second dose being given after three weeks.
The UK has adopted a policy of delaying the second jab of both vaccines by three months, which had led some to question whether the approach would give sufficient immunity.
The trials of the AstraZeneca looked at a longer dosing interval so there was more confidence about that vaccine.
Dr Josie Murray, of Public Health Scotland, said the findings were "brilliant news" and suggested the vaccine programme was working.
Scotland is a good place to do this kind of observational study of how the vaccines are working in the real world.
Its population size and use of individual patient identifiers (known as CHI numbers) enable scientists to track data from the entire population and get results quickly. And while it's still early days, the data indicates that a first dose of either vaccine prevents most people becoming seriously ill.
There are limitations of course. The study only tracked those who were admitted to hospital and whether they had had a vaccine or not.
It didn't count anybody who had died from Covid in a care home, for example. And it didn't look at transmissibility, only the risk of becoming seriously ill.
Other similar studies are being conducted across the UK but this data will be seen as extremely encouraging.