Tokyo's organising committee in 2017 launched a project to collect assorted electronic waste -- including old smartphones and laptops -- from the public to collect metal for the medals.
Recycled metal has also been collected from local Japanese businesses and industry.
In a statement issued on Friday, organisers said the collection was expected to reach its goal and will end in late March.
By November last year, municipal authorities had already collected 47,488 tonnes of discarded devices, with the public handing in another five million used phones to a local network provider.
Organisers had set a target of 2,700 kgs (about 5,950 pounds) of bronze, 30.3 kgs (67 pounds) of gold and 4,100 kg (about 9,040 pounds) of silver.
They hit the target for bronze last June, and by October had more than 90 percent of the gold and 85 percent of the silver.
"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," the organisers said.
Recycled metals have been used in previous years to make Olympic medals, including in Rio where some 30 percent of the silver and bronze in medals came from recycled materials.
The designs for the Tokyo 2020 medals will be unveiled later this year.