The proposed deal with the Edinburgh Schools Partnership (ESP) consortium will be rubber-stamped this week.
ESP is a collection of asset management funds and has no contractor members. The schools were originally built by Amey and Miller Construction.
It will see ESP pay for all structural and defect rectification works and introduce a new independent inspection and monitoring regime throughout the whole estate built under the PPP regime.
The council said: “The proposed settlement sums exceed the associated closure-related costs incurred by the Council.
“Money from the settlement will be used to carry out any further remedial works identified on buildings across the whole Council estate including schools.”
Council leader Adam McVey added: “This has been a lengthy and complex process but I’m pleased that we’ve been able to reach an agreement with ESP.
“This settlement provides significant benefits to our schools and local communities and crucially means the works carried out on the PPP1 schools came at no cost to the Council.
“There will now be additional inspections on the PPP1 buildings and increased opening hours for those facilities.
“Reaching this agreement also means we can avoid potential lengthy and costly legal proceedings for both parties and return to our focus of providing world-class facilities for our young people.”
A spokesperson for Edinburgh Schools Partnership said “This is a significant and positive development for all of the schools impacted by the closures in 2016.
“As the Council report shows we have made strenuous efforts to reach an agreement that reflects our commitment to work in partnership with the Council and avoids the need for difficult and expensive legal action.
“In particular, the contractual enhancements to the existing monitoring framework provide the basis for ESP and our suppliers to continue the process of restoring confidence to pupils, parents and staff.
“We would like to reiterate our apologies to all those affected by the closures and say again that the safety of the children and staff throughout the PPP1 school estate remains our primary concern.”