The move follows a demand from local communities, which have agreed that contaminated soil and other waste will be stored at interim facilities near the Fukushima Daiichi nuclear plant.
The bill obliges the central government to ensure the waste is safely stored, and that it is moved to a final disposal site outside the prefecture within 30 years.
It calls on the government to consider new technologies that might lower the concentration of radioactive substances in soil and reuse waste before final disposal.
The bill revises a law over a state company that deals in the disposal of a toxic substance called polychlorinated biphenyl, or PCB. The revision would allow the firm to engage in businesses related to the storage facilities.
The government plans to have the bill approved by the Cabinet and submit it to an extraordinary Diet session that convenes on Monday.