The riverside building has been named Grainger House in recognition of the time the Scots rower spent training on the River Dee in the 1990s.
With planning permission secured, work is scheduled to start on the four-storey building early this year. Robertson will kickstart the project by demolishing the disused factory that occupies the site on South West Esplanade.
The new premises will span 20,800 square feet of open-plan office space with the capacity to accommodate 200 staff. It will also offer space for 47 cars, including four disabled spaces.
Mark Smith, development director at Robertson Property, a division of Elgin-based Robertson Group, said: "2014 looks to be busy year for Aberdeen, a city which is already experiencing a mini-boom period.
"We are confident in the local market and see this site as the start of redevelopment of the South Dee quarter. We expect strong interest in this project and expect a range of companies to be interested in this opportunity."
The naming of Grainger House is not the first honour Ms Grainger, who won medals in four consecutive Olympic Games, has received from Aberdeen. In 2010 she was awarded an honorary doctorate from the city's Robert Gordon University.
Ms Grainger said: "To have a building named after you is a huge honour and I'd like to wish the project the greatest of success."