That will mean a building project totalling almost 14m, with the cash already secured from the Government.
According to Sheffield Council, schools will need around 250 additional places and it is now expecting to expand 11 primary sites.
The council is intending to expand schools in Netherthorpe, Meersbrook, South Sheffield, Southey, Mosborough and South West Sheffield are where the need is expected to be greatest.
Consultation work has taken place in communities affected, with staff canvassing opinions both at the school gates and in a series of public meetings.
Now further consultation work, about the finer details of how the larger schools will operate, is to take place in the term ahead, with an assurance from the authority it will act only when it has a solution which represents the best interests of the public.
Coun Colin Ross, Sheffield City Council Cabinet Member for Children and Young People's Services, said: "To make responsible plans about schooling we have to keep up to date with changes in the birth rate.
"Otherwise there would not be enough room in local schools for the new intake of children. We are committed to making sure that families can access good local schools in their catchment area, which means creating more places where we expect their to be higher demand in the future."
The council is also confident the building work needed will provide a boost to the city's building trade, which has been hit by the recession.
Some work has already been done in planning how the expansion will work at each of the schools.