The race to host the 2020 Games was whittled down to Tokyo, Madrid and Istanbul after Doha and the Azerbaijan capital Baku were dropped by the IOC in Quebec City on Wednesday.
The IOC will choose the 2020 host city in Buenos Aires in September 2013.
"It is a true honour for Tokyo to be accepted," said Noda.
"Hosting the Olympic and Paralympic Games ... will serve as a symbol of Japan's recovery from last year's tragedy."
A 9.0 magnitude earthquake and giant tsunami in March last year triggered a nuclear crisis at a power plant north of the city. The disaster plunged Japanese sport into chaos, with fears of radiation forcing several major events to be called off or moved, including the world figure skating championships.
Tokyo, which hosted Asia's first Olympics in 1964, lost out to Rio de Janeiro in the race for the 2016 Games after failing to capture enough public support for the bid.
Japanese Olympic Committee President and 2020 bid leader Tsunekazu Takeda said: "We have kept the best and improved the rest from our previous bid.
"We are determined more than ever to produce the best Games plan.
"Tokyo 2020 will be the Games of excellence, staged in the world's most forward-thinking city and will feature world-class infrastructure and technology," added Takeda.