The Fallago Rig project, located 35 kilometres from Edinburgh, features 48 Vestas V90-3MW turbines and has been in operation since January.
The investment was made without the use of third-party debt. Financial terms and the interest that Hermes will hold were not revealed.
EDF will continue to own equity in the wind farm and will still run the site, providing operations, maintenance and asset management services.
Fallago Rig has a long-term power purchase agreement with EDF Energy.
This is not Hermes' first acquisition in Scotland. In June, it bought a 50% stake in the 72MW Braes of Doune onshore wind farm in Stirlingshire from utility company Centrica.