About 32 extra full-time teachers will be recruited for the next school year. Education convener Marilyne MacLaren said one in five pupils in P1-P3 would be in classes of 18 or fewer from August.
The move, which is due to be approved as part of the council's budget next month, comes after the Scottish Government announced it would allow local authorities more flexibility on extending free school meals and increasing nursery hours so they could put more money into meeting class size targets.
Councillor MacLaren said some 1,900 pupils at schools in disadvantaged areas of the Capital would benefit from reduced class sizes.
That would mean that, across the city, a total of 20 per cent of P1-P3 children were in classes of 18 for the new 2010-11 school year, compared with 6.5 per cent at present.
Cllr MacLaren said it had not yet been decided which schools would get the extra staff to bring down their class sizes.
However, she said that once the budget had been approved, officials would be asked to bring forward a list.
Schools that qualify are those where 40 per cent of pupils are eligible for free school meals.
Cllr MacLaren said resources would be targeted where they would have a greater impact.
She said: "I'm very conscious of the lower 20 per cent of children who are not succeeding.
"It is very good to be able to do something that I hope will assist them to reach their full potential."
However, she said in some cases the reductions would be achieved through "team teaching" – classes with more than 18 pupils, but more than one teacher.
She said when Michael Russell took over as education secretary from Fiona Hyslop last month, he had made it clear that team teaching would be an acceptable way of cutting class sizes. Cllr MacLaren said: "I had been arguing the important thing was the teacher-pupil ratio and that if central government was looking for us to do this in all schools, the only way we could oblige was through team teaching.
"The decision to allow team-teaching where appropriate, and the flexibility around the extension of pre-school provision, means it will be a lot easier for us to move forward on the class sizes policy."
The exact numbers of pupils and teachers will be determined once the school rolls for August 2010 are known.
Cllr MacLaren said some minor building alterations may be needed to allow for smaller class sizes, but because of the schools involved extensions would not be necessary.
The council has calculated it would cost about 7m to achieve class sizes of 18 in all its schools, and it does not have the money to deliver that.
The reduction in class sizes comes as headteachers face major budget cuts, but Cllr MacLaren said that as the funding was available due to government flexibility over free school meals and nursery hours, it was not an option to divert it to other areas.