The posts will be lost as part of a restructuring of the regional divisions, with a new Headquarters Support Command being set up in Aldershot, Hampshire.
It follows the Government's strategic defence and security review, which proposed axing 25,000 civilian and 17,000 military jobs.
Once the new base is established, the headquarters of the Army's 2nd Division at Craigiehall, to the north of Edinburgh, will close with the loss of 103 jobs.
In total, 440 civilian jobs will be axed across the UK. Among these, 82 civilian posts will be lost at the headquarters of 4th Division at Aldershot and 63 will go at 5th Division at Shrewsbury.
Armed Forces Minister Nick Harvey last night confirmed the cuts in a response to a written parliamentary question by Shadow Defence Secretary Jim Murphy.
Mr Murphy said: "This is another result of a deeply flawed defence review and will be a big blow to Edinburgh, which is being hardest-hit in this round of cuts.
"Savings must be made, but the defence review, which is already looking out of date, is driven by spending cuts which go too far and too fast, not by the defence needs of our country.
"These sudden cuts will be a blow to morale not just at Edinburgh but across the UK."
Earlier, Mr Harvey said: "This restructuring will remove 440 civilian posts from our regional force structures at both division and brigade levels, and their supporting units.
"The following civilian posts will be cut in each of the divisional headquarters. These losses, which were included in the reduction target announced in the strategic defence and security review White Paper, will be offset by the creation of a number of posts in the new support command headquarters in Aldershot."
He added: "Civilian staff declared surplus will be placed in the MoD's redeployment pool and given assistance to find an alternative post."