The dump at the former experimental nuclear power plant in Caithness will eventually have six vaults, with the first vault expected to open in 2014.
The waste facility is an essential part of the infrastructure needed to complete the £2.5bn decommissioning and closure of the former nuclear research site.
Graham Construction, which has its headquarters in Co Down and offices in Edinburgh and Glasgow, will design and construct two sub-surface vaults for the disposal of solid low-level radioactive waste from the site clean-up.
It is working with consultants I & H Brown and Mott Macdonald.
Up to 100 jobs will be created during the construction phase, with a quarter of the work expected to be sub-contracted to local firms.
The contract will be based on a target cost design and build contract under the NEC conditions.
Building the store within the Dounreay nuclear plant complex was ruled out because of the potential future threat of coastal erosion.