The International Olympics Committee (IOC) made the decision after Japanese prime minister Shinzo Abe asked members to postpone the Games due to measures taken to combat COVID-19.
Their decision ended weeks of speculation over whether the Games would go ahead in July.
The IOC said the Games will be held "not later than summer 2021" but will still be called the 2020 Tokyo Olympics.
"In the present circumstances and based on the information provided by the World Health Organisation today, 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 said in a statement.
Before the official announcement, Mr Abe said IOC president Thomas Bach agreed "100% with him about postponing the games for a year".
The IOC had said it would make a decision in four weeks' time but came under mounting pressure to postpone the Games now.
There had been growing calls for Tokyo 2020 to not take place as the world struggles with the coronavirus pandemic, despite the committee insisting over the past few weeks it would go ahead.
Mr Abe said holding the Games next year would be "proof of a victory by human beings against the coronavirus infections".
Canada and Australia confirmed on Monday they would not be sending their athletes to Tokyo for their own safety, while the British and French governments urged the IOC to make a quick decision.
In the 124 years of the modern Olympics, Games have never been postponed, although they have been cancelled three times - in 1916, 1940 and 1944 due to the two world wars.
The IOC added that the Olympic flame will stay in Japan "to stand as a beacon of hope to the world during these troubled times" and the flame would become a "light at the end of the tunnel".
Sky Sports News correspondent Rebecca Williams said although the announcement will be met with sadness by athletes, it will also come as a relief because it has become difficult to train.
Team GB swimmer Adam Peaty told her a few weeks ago that if Tokyo 2020 went ahead without crowds it would be "really really tough" and they would have to find ways to motivate themselves.
Andy Anson, chief executive of the British Olympic Association, said: "It is with profound sadness that we accept the postponement, but in all consciousness it is the only decision we can support, in light of the devastating impact COVID-19 is having on our nation, our communities and our families."
He said the pandemic has compromised athletes' training and preparation "irreparably" and they need to stop thinking about Tokyo 2020 and "be home and safe with their families".
Sally Munday, CEO of UK Sport, said athletes will not have to pay back any financial investment made in them and they are working to establish how best to support athletes so they are ready for when the Games do take place.
As of the IOC's announcement, 1,140 people in Japan had been confirmed as having coronavirus, while 42 had died.