Members of the International Olympic Committee (IOC) meeting in Buenos Aires yesterday chose the Japanese capital, which previously hosted the Games in 1964, over Istanbul, after Madrid was dramatically eliminated following a first-round tie with the Turkish city.
Crowds gathered in Tokyo broke into wild cheers, despite the result coming in the early hours of the morning nearly a dozen time zones away, television pictures showed.
He told delegates that the situation was "under control", adding: "It has never done or will do any damage to Tokyo."
Fukushima operator the Tokyo Electric Power Co also played down fears of a possible spread of radiation in a separate message.
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Concerns over Fukushima -- seriously damaged in the devastating 2011 earthquake and tsunami that killed more than 18,000 people -- had dogged the bid in the final days but Abe successfully allayed IOC members' fears.
Tokyo -- third in the vote for the 2016 Games won by Rio de Janeiro -- had been the frontrunners originally, as they promised a safe and financially secure Games in what they termed "uncertain times".
The decision means it will be the fourth time that Japan plays host to the Olympics, having also organised hosted winter Games in Nagano (1998) and Sapporo (1972).
Asia will also see successive Olympics, as the South Korean resort of Pyeongchang is hosting the 2018 winter edition.
Madrid had looked to be the city with the momentum coming into the final week after an outstanding presentation to IOC members in Lausanne in July -- and were hoping that like Rio de Janeiro for the 2016 race, they could go on to win.
Doubts about Spain's recession-hit economy persisted to the end and not even some more upbeat news on the issue recently and Prime Minister Mariano Rajoy's pledges that financing would not pose problems convinced enough members that they could deliver.