Four primary schools will reopen to pupils on Monday.
About 3,000 pupils displaced in the school buildings crisis will not be able to return to their own schools until after the summer holidays.
An independent inquiry into the school closures will be held after the summer.
Four primary schools, Pirniehall, St David's, Broomhouse and St Joseph's, will now open on Monday.
Pupils from Rowanfield School will return on Monday 27 June.
This follows the 900 pupils from Oxgangs and St Peter's Primary Schools and Braidburn School who returned to their own schools last month, followed by Firrhill High School, which completely reopened on schedule last week.
The remaining primary schools, - Craigour Park, Forthview, Craigroyston and Castleview as well as Craigmount, Gracemount, Drummond and Royal High Schools will return on 17 August.
Andrew Burns, City of Edinburgh Council leader, said: "We have continued to press the Edinburgh Schools Partnership to bring forward school reopening dates where possible so I'm pleased that we now have 1,000 pupils returning earlier than planned.
"Our priority has always been the safety of our pupils and staff and we have insisted that Edinburgh Schools Partnership and their contractors ensure that our schools are 100% safe to reopen.
"As with the schools that reopened last month, all of the relevant paperwork will be published on our website having been reviewed by an independent expert on behalf of the Council.
"I want again to thank parents for their patience and understanding and teaching staff for their commitment and flexibility during this difficult time."
About 7,600 primary and secondary school children in the capital were affected when the schools, which were all built or refurbished as part of the same public private partnership (PPP) scheme, were closed suddenly in April.
The problem became apparent following an investigation when part of a wall at Oxgangs Primary was blown down.
Edinburgh Council said 1,000 more pupils are returning to schools affected by structural faults after repairs were completed a week early.