It followed an incident on Friday when two men, aged 34-year-old and 25, were detained on Calton Road.
Police also searched a property in the capital, resulting in the recovery of a small amount of herbal cannabis and the money.
A 34-year-old man and a 32-year-old woman have been charged and reported to the Procurator Fiscal.
The drugs were intended for distribution across Edinburgh and enquiries will continue. Detective Inspector David Wright said: "In excess of £20,000 of a Class B controlled drugs has been removed from the streets of Edinburgh."