The agency will position the museum as a UK tourist destination to local, national and international audiences, highlighting the historic importance of the Tudor warship and its restoration.
The attraction will include more than 19,000 artefacts, as well as the warship that has been developed with £21m of Lottery funding.
Kallaway development director Anna Burns said: ‘The Mary Rose story has intrigued many generations for centuries. We are delighted to be a part of such an illuminating heritage project, helping to promote the significance of the Tudor warship and its recovery for generations to come.’
Lincoln Clarke, chief executive of Portsmouth Historic Dockyard, said: ‘This museum is the largest and most significant new addition to the Historic Dockyard since the opening of Action Stations and is the start of many exciting new developments for the site.
‘We were keen to work with a forward-thinking agency on an international scale and we were really impressed by the enthusiasm and creativity shown by the team at Kallaway.’