A major search is under way for the body of Dr Peter Coshan, who was 75 and was last seen in the Seafield Road area of the city shortly before midnight on Thursday.
He was reported missing the following day, prompting exhaustive inquiries by police officers and door-to-door questioning of his neighbours in the city’s Stockbridge.
Two men have now been arrested and charged in connection with his disappearance.
They are due to appear in private on petition from custody at Edinburgh Sheriff Court on Thursday afternoon.
Police Scotland said that officers “can confirm that Mr Coshan is believed to be dead” and they are treating his death as murder.
However, his body is yet to be recovered and an appeal has been launched for anyone with information to come forward so that it can be recovered.
The suspects being held in custody after initially being detained by officers for questioning are aged 27 and 63.
In a direct appeal for information, Detective Superintendent Andrew Patrick, of Police Scotland Major Investigation Team said any potential witnesses can contact the force anonymously via the Crimestoppers charity.
He urged anyone who even suspects that they know something about Mr Coshan’s disappearance to come forward.
Det Supt Patrick said: “Our thoughts are very much with Peter’s family at this difficult time.
“Extensive enquiries are ongoing to trace Peter and I would encourage anyone with any information regarding Peter’s disappearance to contact police as a matter of urgency.
“Any piece of information, no matter how small or insignificant you think it is, could prove vital so please do pass it on to officers.
“We have also set up a website that gives members of the public access to a form to send information directly to the Major Investigation Team.
“You can select to remain anonymous when submitting information.
“The portal can be accessed at: https://mipp.police.uk/operation/SCOT22S27-PO1.”
Dr Coshan was at Fettes College from 1972 until 2005, and was lead on its Duke of Edinburgh Awards scheme for pupils there for 33 years.
He is regularly named in the Old Fettesian Association and is warmly remembered by former pupils and staff as a leading figure at the school.
Dr Coshan is also credited with playing a key role in the development of the Duke of Edinburgh Awards scheme at Fettes, taking it from basic outdoor skills to the modern age and encouraging several generations of pupils to take part.
Former colleagues also said he regularly tutored struggling students because he personally wanted to see them succeed and pass their biology examinations.
Anyone with information can contact Police Scotland on 101 quoting incident number 1745 of 12 August, 2022 or the inquiry team can be contacted anonymously via Crimestoppers on 0800 555 111.