A project was started in 2017 to collect enough electronic waste, including old smartphones and laptops, to implement the scheme.
The aim was to collect 30.3kg of gold, 4,100kg of silver and 2,700kg of bronze.
Organisers say they are on course to reach those targets in March.
The target for bronze was met last June, while the organisers had more than 90% of the gold and 85% of the silver by October.
Tokyo 2020 will release the designs of its medals later this year.
The recycled metal has been collected from the Japanese public as well as businesses and industry.
By November 2018, 47,488 tonnes of discarded devices had been collected, with the public handing in another five million used phones to a local network provider.
“It is estimated that the remaining amounts of metal required to manufacture all Olympic and Paralympic medals can be extracted from the devices already donated,” Tokyo 2020 organisers said in a statement.
At the 2016 Olympics in Rio, about 30% of the silver and bronze in medals came from recycled materials.