Edinburgh won the battle to become the home of the new government-backed body, which will help pioneering environmental projects get off the ground by providing finance.
But so far the bank has not decided on a permanent home in the Capital.
The council has stepped in to provide a base on an open-ended arrangement until a long-term headquarters is secured.
It is understood two or three staff have already moved into the new ground-floor accommodation at Waverley Court and numbers will gradually expand to around ten.
Waverley Court has capacity for 1800 people. A council source said finding room for ten extra people had not been a problem.