Police confirmed the 65-year-old man’s identity as Roderick Lakin from London.
Sergeant Keith Denholm of Road Policing said: “We offer our sincere condolences to Roderick’s friends and family at this sad time, and I’d like to thank the public for their continued support while our investigation into this collision continues.”
The news comes as it emerged the driver of the double-decker bus could be facing dismissal.
Mr Lakin was left in a critical condition on August 19 after being knocked down by the number 41 Lothian bus at the junction of Frederick Street and Princes Street.
It is understood Lothian Buses has recommended the driver be sacked – but the decision has yet to be made final and can still be appealed. The reasons behind its recommendation are still unknown.
Mr Lakin was rushed to Edinburgh Royal Infirmary after the accident and then transferred to the Western General Hospital, where he passed away on Friday evening.
It is understood that the experienced driver has not been allowed behind the wheel of a bus since the incident. One bus driver told the Evening News that he and his colleagues were planning a walk-out if the sacking went ahead. But union bosses dismissed the claim and insisted they were not aware of any strike action.
Duncan McBride, chairman of the Lothian Buses branch of Unite, said: “As far as I’m aware the investigation by Lothian Buses is still ongoing. I have not been informed of anything.”
The horror crash happened at 10.45am on Wednesday, August 19, and saw police close the entire stretch of Frederick Street and a section of Princes Street to the West End. Frederick Street remained cordoned off by road collision investigators until around 5pm, with the bus – which had a large crack in its lower windscreen – removed shortly beforehand.
A Lothian Buses spokesman said: “An investigation has been carried out in line with procedures agreed with trade unions and the appropriate processes are now being followed. It’s important to stress that this process has not yet been exhausted.”
The accident comes just months after the junction’s pedestrian crossing was condemned as a “safety hazard” by campaigners. Pedestrian rights group Living Streets Scotland raised concerns after revealing walkers have just six seconds to cross at the green man.
Jim McFarlane, chair of Lothian Buses, added: “We are deeply saddened and our thoughts are very much with the family at this time.”