A winner will be chosen later this month, the Japan Sports Council said in a statement.
"(The winning design) will be selected by the end of December after further examination by a committee consisting of architectural experts and ministers," said Council president Kazumi Daito.
In July, Prime Minister Shinzo Abe announced that the government was ditching
Iraqi-British architect Zaha Hadid's "bike helmet" stadium design, which had been projected to cost 150 billion yen ($2.02 billion).
Abe said the scrapping of the design meant the stadium would not be ready in time for the 2019 Rugby World Cup, but said he was "certain" that the project would be ready in time for the 2020 Olympics and Paralympics.
A spokesman for Zaha Hadid Architects blamed increases in construction costs in Tokyo and the difficult of working to a fixed deadline for the stadium's spiraling price tag.
The firm claims refinements they proposed to the original design would have allowed stadium construction to have already got underway and that their new design would have been delivered in time for the 2019 Rugby World Cup. "There are now serious risks of a rushed process," said the spokesman, warning a new design could require expensive conversion after the 2020 Games.
The firm added: "It is disappointing that the Government did not even consider working with the existing design team... The rules of entry to the new competition restricted the existing design team, as well as many other Japanese and international architects and contractors that wished to take part, from entering."
Japanese architects had been scathing of Hadid's design, with leading architect Arata Isozaki writing an open letter to the government body in charge of the games that the sight left him "in despair" and warning the stadium would be a "disgrace to future generations."
The two stadium plans unveiled this week are expected to cost around 154 billion yen (1.26 billion) and will accomodate 80,000 people.
The steel and wood Design A resembles traditional Japanese temples, and stands at a relatively short 50 meters (164 feet) with its main sports field sunken under the ground.
Design B is taller, with more glass. It is intended to reflect traditional Asian concepts of the five elements: fire, earth, metal, wood and water, according to a statement.
The Sports Council didn't reveal who the architects were.
Whichever plan is eventually chosen, construction is due to be completed by November 30, 2019, 266 days before the Olympics Opening Ceremony.