The work will see the firm demolish the existing listed council building in Market Place, which was originally constructed in the 1860s.
24,000 sq ft of contemporary office space is to be built in its place.
The new building will consist of three floors to the front and two to the rear.
It will house the Social Care and Education Culture and Sport departments.
The new facility will be clad in timber to the rear, with stone and glazing to the frontage, and will also feature a clock face.
Morgan Sindall will also refurbish and restore the adjoining curved Stafford Place Buildings which were built in the 1820s.
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The listed façade will be preserved following consultations with Historic Scotland.
David Sutherland, Project Manager at The Highland Council, said: "The development has been a long time in the planning and will deliver a state of the art facility for the Council to do its business with its customers, whilst ensuring efficient use of resources both in buildings and staff. The location is central to maintaining not only the viability of the town centre but also that of neighbouring businesses that depend on Council staff for much of their trade."
Neil Duncan, area director for Morgan Sindall, said: "This project signals the beginning of a major transformation of Wick, and we are pleased to be working with The Highland Council to deliver this significant development. Whilst the building will be modern in design, it will complement Stafford Place and provide a high standard of office accommodation to best meet 21st century working needs.
"A project of this size will have a big impact on the local economy and we always look to support the communities in which we work. We will be aiming to appoint a number of local sub-contractors and, in turn, recruit apprentices from the area during the 18 month project."
The offices are due for completion in autumn 2014.
(IT)
