It beat off rival bids from BAM Nuttall, Black & Veatch and a Morrison/Balfour Beatty/Morgan Sindall joint venture to the £100m-plus job. Rok was also on the shortlist until its collapse.
Subject to NDA approval and completion of a number of procedures, the contract award is expected by the end of March to allow a start on the two-year construction programme this autumn.
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.
Client Dounreay Site Restoration actually has planning consent for up to six vaults but hopes to reduce the number needed through waste minimisation practices in decommissioning.
Up to 100 jobs will be created during the construction phase, with a quarter of the work expected to be sub-contracted to local companies.
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.
Disposal facilities will consist of a series of shallow engineered vaults to be built in phases, up to a maximum of six, a grouting plant constructed within the existing site and an administration block.
Each vault will measure approximately 80 x 45 m, with a depth of approximately 20m.
This facility is required for disposal of up to a maximum of 175,000 cubic metres of solid low-level waste which is expected to be generated during the decommissioning of the site.
In a separate plan Dounreay Site Restoration will also restore a nearby area of land designated as a rubble dump during the construction and operation phases of the site.
An estimated 70,000m3 of material from the construction and demolition of buildings was deposited in the area beyond the eastern perimeter of the site from 1960.
The site, known as Landfill 42, was taken out of use in 2005 and needs to be restored under environmental and planning regulations.
This will involve repositioning approximately 16,000m3 of material and the construction of a new sea defence.
A substantial impermeable membrane and an estimated 25,000 tonnes of rock will be used in the closure works.
The work is expected to cost £2m and, subject to regulatory controls, is due for completion by the end of 2011.