The man was named as Rev Tom Sinclair, 76, a commissioner from the Presbytery of Lewis at the General Assembly this week.
He was on Waverley Bridge walking across the entrance road to the station, when he was hit.
The incident happened when the Assembly finished for the day.
The Moderator, the Rt Rev John Chalmers remembered Mr Sinclair and his family in prayers at the start of the Assembly this morning and assured the family that the prayers of the whole Church would continue to be with them.
He said: “The news of Tom’s death in such tragic circumstances came as a terrible shock to the General Assembly. Tom Sinclair loved the Church of Scotland and loved the General Assembly. We mourn his loss and we commend his wife and family to the care of the community of faith and to the grace God.
“Tom’s death is a painful tragedy for his wife and family and will come as real blow to the Presbytery of Lewis which he was still serving as Presbytery Clerk.”
Mr Sinclair, originally from Glasgow, was Clerk to the Presbytery of Lewis for over 30 years. He is survived by his wife Pam and a son Jonathan, 43, who lives in Edinburgh.