It follows the scrapping of a high-profile plan by architect Zaha Hadid earlier this year.
"Today, the Japan Sports Council reported that Plan A was chosen for the new National Stadium design," Abe said Tuesday, referring to the latest proposal by famed Japanese architect Kengo Kuma and Taisei Construction Corporation.
"The ministerial meeting has checked the selection was made in an appropriate manner. This is an excellent plan that satisfies the principle philosophy, construction, deadline and cost of the Olympic plan."
The steel and wood concept resembles traditional Japanese temples and stands at a relatively short 50 meters (164 feet) with its main sports field sunken under the ground. The stadium is estimated to cost 154 billion yen ($1.26 billion) and will accommodate 80,000 people.
Abe urged the new main stadium to be the "best in the world," representing Japanese-style design and providing a "legacy that we can be proud of for the next generation."
Two designs were submitted
earlier this month after original plans by Iraqi-British architect Hadid were scrapped in July. Her concept had attracted criticism
with various prominent architects and the public saying it looked like a bike helmet or a turtle.
'Not about design or budget'
While the government cited ballooning costs as the reason to reopen the stadium design bid -- the costs of Hadid's designs had at one point grown to 150 billion yen ($2.02 billion) from the original proposal of 162 billion yen ($1.31 billion) -- a statement from Zaha Hadid Architects sent out after the new design was chosen argued that budget was not the true reason they lost the contract. They insisted they had made modifications to address financial concerns.
"Sadly the Japanese authorities, with the support of some of those from our own profession in Japan, have colluded to close the doors on the project to the world," it said.
"This shocking treatment of an international design and engineering team, as well as the respected Japanese design companies with whom we worked, was not about design or budget. In fact much of our two years of detailed design work and the cost savings we recommended have been validated by the remarkable similarities of our original detailed stadium layout and our seating bowl configuration with those of the design announced today."
It went on to say that construction would have already be underway if they had been allowed to develop the original design, and the new design risks not being ready in time for the 2020 Olympics.
Although the stadium will not be completed in time for the 2019 Rugby World Cup, Abe has said it will be ready for the 2020 Olympics and Paralympics. The project is due for completion by November 30, 2019 -- 266 days before the Olympics opening ceremony.