Officers were called out address on Portland Street amid reports of a man causing a disturbance and refusing to leave.
North Fort Street was also sealed off and the gas supply was switched off as a “precautionary measure”.
A 53-year-old man has been arrested and will be reported to the Procurator Fiscal in due course.
A Police spokesman said: “Police Edinburgh were called to an address in Portland Street in Leith at around 10.30am on Sunday, June 19, following a report of a male causing a disturbance and refusing to exit a property.
“Specialist officers assisted by local officers attended the scene and brought the matter to a safe and peaceful conclusion at around 1.45pm. As a precautionary measure the local gas supply was switched off during the incident.
“A 53-year-old man has been arrested and will be reported to the Procurator Fiscal in due course.
“Members of the public are thanked for their patience and cooperation over the course of the police response.”