The logo, called Harmonized Chequered Emblem, replaces the first choice which was thrown out last year after the designer was accused of plagiarism.
The designer denied stealing the idea.
Organisers said the new design used traditional Japanese colours and patterns to represent the intercultural themes of the Games.
"It incorporates the message of 'unity in diversity'," they said, and the idea that the Games "seek to promote diversity as a platform to connect the world".
When designer Asao Tokolo found out he had won the re-opened contest he said "my mind has gone blank".
"I put a lot of time and effort into this design as though it was my own child."
The first design was rejected after Belgian artist Olivier Debie alleged it copied his design for a theatre logo.
The Games organising committee never agreed to the allegation of plagiarism but said there were too many doubts over the emblem for it to be used.
The logo dispute came shortly after Tokyo decided to scrap the designs for the main Olympic stadium because of spiralling construction costs.
A cheaper design, by Japanese architect Kengo Kuma, was chosen in December last year.
Japan's Olympic organisers have unveiled the new official logos of the 2020 Tokyo Olympic and Paralympic Games.