The facilities cost a combined total of more than £300m
Construction is expected to begin next year on the largest store and treatment plant ever to be built in Scotland to deal with radioactive waste.
The facilities costing a combined total of more than £300m will be built on land next to the Dounreay nuclear power complex in Caithness.
They were approved by Highland Council and forwarded to the Scottish Government for consideration.
Ministers have decided not to call in the planning applications.
However, they have asked the local planning authority to include an extra condition about the establishment of a community benefit fund as part of its approval of the stores.
Work is due to start next year on the treatment plant and construction on the store is to begin in 2011.
Dounreay Site Restoration Limited (DSRL) said the store will hold almost 200,000 cubic metres of waste from the defunct Caithness nuclear energy plant.
People living close to the proposed site on a former military airfield had raised concerns.
These included worries the dump will devalue neighbouring properties.
Building the store within the Dounreay site was ruled out because of the potential future threat of coastal erosion.
Solid and liquid intermediate-level radioactive waste will be processed in a new treatment plant, known as D3900, where it will be mixed with cement and set inside drums and crates.
Once set, the containers will be moved to the adjoining storage area where they will be held pending Scottish policy for the long-term management of this type of waste.
The first of the vaults of the store are expected to be ready to receive waste in 2014.
Tony Trayner, head of construction at DSRL, said the facilities were key to the clean-up of Dounreay.
He said: "An essential element of any decommissioning project is being able to deal with the radioactive waste that it generates and these new facilities will give us that capacity through to the end of our programme."