The council is transferring the Rothwell and Chapeltown sites to private providers, which the authority said would eventually save £500,000 per year.
The new operators will sign 10-year leases for the buildings and rent them for a combined cost of £72,000 per year.
A 5% fee increase was also expected to raise £78,000 per year across the remaining authority controlled sites.
The Shepherds Lane centre, in Chapeltown, is to be taken over by Sunshine Community Nursery, which is rated as an “outstanding” provider by Ofsted.
The Rothwell nursery, on Cornwall Crescent, will be run by Sweet Peas Day Care and Teaching, which has a “good” rating.
Despite the reassurances provided by the review’s outcome, Mr Wood said parents feared the nurseries could be targeted again.
“They have been salami slicing Little Owls for years, so there is so much uncertainty that still hangs over us.
“Unless council budgets are rectified, nurseries are an easy target.”