1235 GMT April 04, 2020
The event, due to begin on July 24, will now take place "no later than summer 2021", the International Olympic Committee (IOC) confirmed, according to BBC Sport.
"I proposed to postpone for a year and [IOC] president Thomas Bach responded with 100 percent agreement," Japan's Prime Minister Abe Shinzo said.
The Tokyo Paralympic Games will also be postponed until 2021.
The event will still be called Tokyo 2020 despite taking place in 2021, the IOC said.
In a joint statement, the organizers 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.