The event, due to begin on 24 July, will now take place “no later than summer 2021”.
“I proposed to postpone for a year and [IOC] president Thomas Bach responded with 100% agreement,” Japan’s Prime Minister Shinzo Abe said.
The event will still be called Tokyo 2020 despite taking place in 2021.
In a joint statement, the organisers of Tokyo 2020 and the IOC said: “The unprecedented and unpredictable spread of the outbreak has seen the situation in the rest of the world deteriorating.
“On Monday, the director general of the World Health Organization, Tedros Adhanom Ghebreyesus, said that the COVID-19 pandemic is ‘accelerating’.
“There are more than 375,000 cases now recorded worldwide and in nearly every country, and their number is growing by the hour.
“In the present circumstances and based on the information provided by the WHO today (Tuesday), the IOC president and the prime minister of Japan have concluded that the Games of the XXXII Olympiad in Tokyo must be rescheduled to a date beyond 2020 but not later than summer 2021, to safeguard the health of the athletes, everybody involved in the Olympic Games and the international community.”
The IOC had given itself a deadline of four weeks to consider delaying the Games but there had been mounting pressure from a host of Olympic committees and athletes demanding a quicker decision.
Canada became the first major country to withdraw from both events on Sunday, while USA Track and Field, athletics’ US governing body, had also called for a postponement.
The Olympics have never been delayed in their 124-year modern history, though they were cancelled altogether in 1916, 1940 and 1944 during the two world wars.
Major Cold War boycotts disrupted the Moscow and Los Angeles summer Games in 1980 and 1984.
The Tokyo 2020/IOC statement continued: “The leaders agreed that the Olympic Games in Tokyo could stand as a beacon of hope to the world during these troubled times and that the Olympic flame could become the light at the end of the tunnel in which the world finds itself at present.
“Therefore, it was agreed that the Olympic flame will stay in Japan. It was also agreed that the Games will keep the name Olympic and Paralympic Games Tokyo 2020.”
The agreement comes as the British Olympic Association (BOA) was meeting on Tuesday to discuss the matter.
BOA chairman Hugh Robertson had already said Great Britain was unlikely to send a team to Tokyo this summer.
‘The Olympics has never had a challenge like this’ – analysis
Dan Roan, BBC sports editor
This is arguably the biggest decision sport has seen in peacetime.
For weeks now it has looked inevitable, and many will ask why it has taken until now.
With athletes unable to train safely, and the calendar of Olympic and Paralympic qualification events decimated amid travel restrictions and lockdowns, a postponement or cancellation emerged as the only viable options.
Faced with the unenviable task of reorganising a sprawling mega-event that has already cost at least £10bn in preparations, the IOC and Japan had hoped to buy themselves some time to consider their next step.
But with Olympic committees and athletes increasingly frustrated and confused at what some saw as delaying tactics, the decision was effectively taken out of the organisers’ hands, and just 48 hours after the IOC said it was giving itself four weeks to mull it over, we now know the Games cannot go on as planned.
The ramifications will be significant. It’s a huge blow to Japan, and the country will now have to spend yet more money. Commercial contracts will have to be unpicked and the availability of venues revisited. A crowded sporting calendar will have to be flexible. And the IOC, sports federations, broadcasters, sponsors and a myriad of other related businesses will have to wait an additional year for the financial bonanza that the event generates.
The Games has had to deal with many challenges over the years, from terrorism and boycotts to war and doping. But nothing quite like this.