In April, 17 schools were shut by officials due to concerns over their structural safety.
The schools were delivered following a £360 million deal between the council and a private finance consortium under the Public Private Partnership 1 (PPP1) scheme.
Each school had been built by Miller Construction, which Galliford Try acquired in 2014.
Eight schools are now expected to reopen in the coming weeks with Oxgangs Primary, St Peter's and Braidburn being the first ones to reopen to pupils next Tuesday, 24 May.
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An independent senior figure is expected to be appointed to chair the inquiry, which will cover all aspects of the closures. However, the specific terms of reference will be discussed with political group leaders later this week and agreed with the chair prior to getting underway.
Council leader Andrew Burns said: "It is important that we have an independent chair for this inquiry; one who commands respect within the construction industry.
"The terms of reference will be thorough and we want the report to get to the heart of this issue and see what lessons can be learnt, not just here in Edinburgh, but across Scotland.
"When the issue came to light, our first priority was safety of pupils and staff, the second was getting pupils back into education, the third is getting the schools reopened and it is not until this has happened that the inquiry will begin.
"Naturally, we want the report to come back as quickly as possible and I would expect it to be complete in a matter of months. We want and deserve answers as to how this has happened – as do parents across the city."
(LM/JP)
