Dudley Metropolitan Borough Council is currently responsible for 20 children's centres but says it needs to cut its current £3m annual budget by nearly half.
It will retain responsibility for five centres, but they will be converted into "family centres" that offer early help support for children aged up to 18. Responsibility for the remaining 15 children's centres will be handed to local schools.
Dudley Council's lead member for children's services Ian Cooper said the restructure would save the service £1.4m from its 2016/17 children's centres budget of £3m - a reduction of 46.7 per cent.
"The direct savings resulting from transferring the premises costs to schools are estimated to be £177,000," he said.
He added the changes would allow "support services to be delivered more holistically and efficiently, directly to the communities in which schools are based".
A report on the proposals reveals that schools running the 15 transferring centres have been given a clear instruction that the provision "must continue in the same way" in order to avoid the imposition of any financial penalties from central government.
As part of Sure Start funding arrangements, the Department for Education can reclaim capital funding if money provided for early years services no longer meets the original aims of the funding through a so-called "claw-back" mechanism.
Two of the children's centres have already transferred to schools. The council plans to phase in the new arrangements for all centres by September 2017.
