Bury it underground. The amount of waste generated by nuclear power is a fraction of 1% of all the toxic waste generated by heavy industry. The entirety of the United States' nuclear waste from electricity generation occupies a volume the size of a football field in footprint and 10 yards high [1]. A coal plants generates this much waste every hour.
You reprocess it to remove all the stuff that isn't actually "waste" because it's usable as fuel. What remains presents a much smaller storage problem which has known working solutions.
1. https://www.nei.org/fundamentals/nuclear-waste