The Japanese capital won what one insider had called a "least-ugly" contest by most effectively covering its blemishes. Rival Madrid has been laid low by the economy and Istanbul has been beset by anti-government protests.
Tokyo won by a landslide, 60 votes to Istanbul's 36, after Madrid was eliminated in a first round of voting.
Abe, who left early from a Group of 20 summit in Russia to make his pitch at the meeting in Buenos Aires, promised the roughly 100 members of the International Olympic Committee that concerns about the leaking Fukushima nuclear plant 140 miles (230 km) from Tokyo were unfounded.
Fixing IOC members with a level gaze, he said: "It has never done and will never do any damage to Tokyo. There are no health-related problems until now, and nor will there be in the future - I make the statement to you in the most emphatic and unequivocal way."
The plant's operator has said hundreds of tonnes of radioactive water are pouring into the Pacific Ocean each day, and radiation levels have spiked.
Abe's government said this week it would spend almost half a billion dollars to try to fix the water crisis. He told the IOC on Saturday, "Let me assure you the situation is under control."
Tokyo won the right to stage the sporting extravaganza for the second time, having hosted in 1964 when the Games first went to Asia. On that occasion, Abe's grandfather, Prime Minister Nobusuke Kishi, led the bid to bring the Games to Japan.
Tokyo in its pitch highlighted its solid finances and strong track record of delivering on promises. Olympic President Jacques Rogge described it as "a safe pair of hands."
The next summer Olympics will be hosted by Rio de Janeiro in 2016, and the preparations for that Games have been plagued by delays and complications.
Moreover, the Tokyo bid capitalizes on the potential of the Asian continent, with its increasingly consumer-focused economies.
Winning the Games was an enormous prize after two years of intense lobbying and tens of millions of dollars spent, and Abe was thrilled.
"I would like to thank everyone in the Olympic movement and we will host wonderful Olympic Games," a beaming Abe told Reuters seconds after the result.
Bid leader Tsunekazu Takeda was in tears as he said, "It is a great honor that Tokyo has been chosen.
For Istanbul, it was its fifth unsuccessful bid in the last six votes to host a summer Olympics.
The city had pitched itself as a new region for the Games, the crossroads of Europe and Asia, and as a vehicle to help foster peace in the Middle East. But the conflict in neighboring Syria and recent anti-government demonstrations in Turkey overshadowed the bid.
Istanbul bid sports director Alp Berker was searching for a reason for rejection as he told Reuters, "I don't know. ... there are too many variables, maybe it's the timing, maybe it's something else."
When asked if the Syrian crisis had damaged their chances, he said: "We tried to tell them it was not the case, because it's a global issue. Really, I don't know what the members are thinking when they're pushing the button."
IOC vice-president and presidential candidate Thomas Bach described the decision as new versus old.
"I think it is an election between a traditional candidature and new grounds, and today it was the traditional candidature that won," he told Reuters.
Madrid, which had pitched a safe, affordable, "sensible" bid, was eliminated in a secret vote pitting it against Istanbul after the two cities tied behind Tokyo. Madrid's attempt to host 2020 was its third consecutive try.
Tokyo is planning to incorporate existing venues and has estimated a non-Games budget of about $4.4 billion, compared with $3.4 billion for the actual event.
It already has a war-chest of some $4.5 billion in the bank.
The victory is expected to boost Abe's popularity, and could potentially spur his signature pro-growth policies for the world's third-biggest economy. A successful Tokyo bid should boost confidence as well as spur construction and tourism.
Official Voting Results
Tokyo - 60
Istanbul - 36
- Politics & Government