Processes for desalting glycerol-rich solutions or process streams using electrodialysis are provided. The glycerol-rich process streams are typically byproducts from the production of biodiesel. Following electrodialysis, the resulting aqueous salt solution is placed in a water splitting cell to recover the acid and base components of the salt. These acid and base components, in turn, can be reused in other processes, such as biodiesel production.