The building, set to open to the public next spring, will be the first in a British botanic garden dedicated to growing Alpine plants in limestone.
In the existing alpine house, plants are in pots but in the new structure they will be in their natural rockface environment.
The move will help conservation of alpine plants across the world. For 140 years the organisation has pioneered the growing of wild-collected alpines. However, severe space restrictions mean the vast majority of plants held in Edinburgh have never been on public display.
John Mitchell, alpines supervisor at the Botanics, said: “Now, we have an opportunity to show how alpine growing techniques have evolved in the last 30 years.
“The new structure will sit next to and complement the traditional house by showcasing the latest techniques in the cultivation and care of alpines.”