The 17 schools were shut after structural defects were discovered inside some of the buildings in April.
Contractors have now completed remedial works and handed back the final two schools, Community High and The Royal High, to the city council.
The schools were built in 2005 under a £360 million private finance deal with the Edinburgh Schools Partnership (ESP).
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An independent inquiry is underway and is expected to finish before the end of this year. Construction and procurement industry expert John Cole CBE has been appointed to lead the inquiry.
Council Leader Andrew Burns said: "I'm delighted that all of our pupils affected by the closures will be back in their own schools next week as we promised parents we would try to achieve this.
"Our priority has always been the safety of our pupils and staff and we insisted that ESP and their contractors ensure all our schools are 100% safe to reopen. The next steps now are to establish exactly what went wrong with these schools.
"Clear and thorough terms of reference set out exactly what we are aiming to achieve through this inquiry. We want to find out what went wrong and are determined to see what lessons can be learned, not just here in Edinburgh but across Scotland and the UK."
(LM/MH)
