Priority has been given to secondary pupils in fourth, fifth and sixth year who are just three weeks away from sitting key exams.
All primary pupils are due to return by next week but uncertainty remains over arrangements for S1-S3 pupils.
A total of 17 schools in the city did not reopen after the Easter break.
About 7,600 pupils were affected by the closures with five secondaries, ten primaries and two additional support needs schools shut due to concerns over structural issues.
All of the schools, which are about 10 years old, were constructed under the same public private partnership contract.
The council said on Tuesday evening it hoped to have all pupils back in "places of education" by next Tuesday - Monday 18 April is a bank holiday in the city.
Senior pupils from four of the high schools, as well as children from two primaries were due to return to classes on Wednesday morning.
Some will go back to their own classrooms but others will transfer to alternative schools where they will be taught by their own teachers.
The arrangements put in place by the City of Edinburgh Council will see:
About 2,300 S1 to S3 pupils still do not know when they will return to class. The council has said it will give further details on that later this week.
The problems were first uncovered in January when a wall at Oxgangs Primary collapsed during high winds.
Further closures were prompted on Friday after workers repairing serious structural issues at the primary found "further serious defects" with the building.
The city council has said urgent work would need to be carried out on at least four of the schools: two high schools Gracemount and Craigmount, and two primaries - Oxgangs and St Peter's.
The initial problem was discovered with wall ties, which hold the outer and inner walls together, at Oxgangs Primary School.
An additional issue on Friday was then found with head ties, which hold the top of the walls to the steel roof frame, at all four schools.
Concerns had been raised about the need to accommodate senior pupils who are due to sit exams soon and have coursework and assessments to complete.
With about 5,000 pupils facing a third day off school on Wednesday, parents were also continuing to express anger and frustration at the cost and hassle involved in arranging extra childcare.
Offers of support to the council to accommodate pupils affected have come from organisations including Hibernian Football Club, the Scottish Parliament, Edinburgh University and NHS Lothian.
More than 2,000 pupils whose schools in Edinburgh have been closed because of safety concerns are due to return to classrooms later.