The experienced former Hearts manager will work alongside City boss Gary Jardine, helping with player recruitment and acting as a sounding board.
City are the newest team in the SPFL, winning promotion to League 2 last summer after defeating East Stirlingshire in the Pyramid play-off.
Jefferies, 66, who led Hearts to their Scottish Cup triumph in 1998 and has also managed Bradford City, Kilmarnock, Falkirk, Dunfermline and Berwick Rangers, said he was looking forward to the challenge
“During my chats recently with the club I’ve been impressed with their ambition and plans going forward and I look forward to helping them in areas which they feel they need support,” he said. “I hope my years of experience can help them and I look forward to the challenge.”
Jardine said he was pleased to be able to draw on Jefferies’ experience.
“It’s another fantastic step in the right direction for the club,” Jardine said. “If we have lacked anything as a club since making the step up it would be experience.
“Jim coming in gives us that in abundance having been involved at every level of the game in Scotland and that can only improve Edinburgh City and on a personal level myself and the coaching staff.”