The rollout of the Pfizer-BioNTech Covid-19 across Europe is under way following approval on Monday by the European Medicines Agency.
A 101-year-old woman in an elderly care home became the first person in Germany to be inoculated against coronavirus.
It comes a day before the official vaccination campaign was scheduled to get under way in both Germany and the EU.
Edith Kwoizalla was one of around 40 residents and ten staff in a care home in the eastern state of Saxony-Anhalt to receive the jab.
The Pfizer-BioNTech vaccine became the first to get the go-ahead for use in the West, when Britain gave its approval on 2 December.
As other nations from the United States to Saudi Arabia to Singapore followed suit, Germany impatiently prodded the EU's drugs regulator, the European Medicines Agency, to bring forward its decision from 29 December.
The EMA finally gave its green light more than a week early, on 21 December.
On the same night, the European Commission declared that the entire bloc would start the inoculation operation from Sunday, December 27.
"For us, every day counts," said Immo Kramer, a vaccination centre official for the region, told MDR public television.
Today, tens of thousands of vaccine doses were delivered to the regional health authorities, who then distributed them to local vaccination centres.
Elderly care home residents, people aged 80 and over and care staff will be the first to get the jab.
German Health Minister Jens Spahn called it a "day of hope".
"The vaccine is an essential key in conquering the pandemic," he told a news conference.
"It is the key that will allow us to take back our lives," but he warned that getting everyone immunised would be a "long-haul" effort.
Elsewhere, Spain received its first doses of the vaccine, a day before the country is set to begin its immunisation campaign.
A refrigerated truck arrived at Pfizer's warehouse in Guadalajara in central Spain with the shipment, three days after it left the company's factory in Puurs in northeast Belgium, the health ministry said in a statement.
After repackaging, the vaccines will be redistributed to Spain's 17 autonomous regions so that vaccination can begin across the country as planned on Sunday, it added.
Spain will receive 4.5 million Pfizer vaccine doses over the next 12 weeks, enough to vaccinate some 2.3 million people, according to the ministry.
It plans to vaccinate elderly residents and staff in nursing homes first, then health workers and other vulnerable people, such as the elderly and people with underlying health conditions.
Hungary starts coronavirus vaccinations
Hungary started vaccinating healthcare workers against the coronavirus with the Pfizer-BioNTech Covid-19 vaccine, a day earlier than in most other countries in the European Union.
Hungary received a first shipment of coronavirus vaccines this morning that will be enough to inoculate 4,875 people, state news agency MTI reported.
"We have started the inoculations among healthcare workers according to a plan defined earlier," a government spokesman said.
The first worker to receive the shot was Adrienne Kertesz, a doctor at Del-Pest Central Hospital.
The distribution of the Pfizer-BioNTech shot presents tough challenges because it uses new mRNA genetic technology, which means it must be stored at ultra-low temperatures of around -70C.
Earlier this month, the UK became the first country in the world to roll out the Pfizer-BioNTech vaccine.
As of today, Hungary had reported 315,362 Covid-19 cases with 8,951 deaths. More than 6,000 people are still in hospital with the virus, straining the healthcare system.
First Covid vaccine doses arrive in France
France's first doses of the Pfizer-BioNTech coronavirus vaccine were delivered to the Paris hospital system's central pharmacy outside the capital.
After more than 62,000 Covid-19 deaths in France, shots are set to begin with people in two elderly care homes tomorrow.
A refrigerated truck brought the roughly 19,500 doses from the Pfizer factory in Puurs to Paris, the capital's APHP hospital authority said, with pharmacy chief Franck Huet calling it a "historic" moment in the pandemic.
After repackaging in Paris, the vaccines will be delivered to a long-term care unit at a hospital in Sevran, outside the capital, and an old-age care home in Dijon, in eastern France.
The first EU deliveries come after the European Medicines Agency (EMA) gave the Pfizer-BioNTech shot its green light on Monday and France's HAS health authority in turn on Thursday.
Countries are especially eager to begin their vaccination campaigns as a new strain believed to be more infectious spreads from Britain. A first case was identified in France yesterday.
But large-scale inoculations for residents and staff in France's 7,000 elderly care homes will not begin until early next year.