The job was secured for £16.3m and involves building a museum above the number three dock in Portsmouth.
Warings picked up the enabling works last year and won the main contract through an electronic tendering process.
The final works on the £35m museum project include the building frame and envelope as well as the services installations, together with the interior fitting out.
There will be some contractor design and coordination of certain other project works as part of the deal.
An option to carry out further works in 2016 will be included.