Children's television programmes including Blue Peter and Newsround will be moved off BBC1 and BBC2 as part of the corporation's cost-cutting measures.
The shows will move to digital channels CBBC and CBeebies as part of the Delivering Quality First scheme.
The plans, part of a process which has seen the BBC commit to saving billions of pounds from its budget after the annual licence fee was frozen at £145.50 for six years, were rubber-stamped by the BBC Trust.
The trust's response said the impact on children would be "very low", stating: "Only around 7% of CBBC's target audience currently watch CBBC content on BBC One and BBC Two but do not also watch the CBBC channel." But it admitted the move could cause "short-term confusion" and would need "sufficient cross-promotion and marketing".
A trust spokesman said children's programmes were "absolutely fundamental to the BBC".
He said: "Only a very small percentage of children still solely watch these programmes on BBC One and BBC Two alone, so moving them to digital channels is merely following current viewing patterns and reflects the fact that CBeebies and CBBC will be universally available on digital TV from the end of this year. We have asked the Executive to ensure the changes are prominently publicised well in advance."
The trust also confirmed proposed savings in local radio have been cut from £15 million to £8 million. Its chairman Lord Patten said the report was "the end of a lengthy process".
He said: "Delivering the changes we have approved will be challenging, but they are necessary. We've listened carefully to the views of those who care about the BBC and taken our time to get this right, encouraging the Executive to amend plans where we think they need further thought, as the changes to local radio proposals show.
"Our focus now is to ensure that audiences notice as little change as possible to the services they know and love, and we will be monitoring audience reactions very carefully through our ongoing programme of reviews and reports."
A BBC spokesman said: "We welcome the BBC Trust's full approval of our Delivering Quality First proposals. The coming years will involve a significant effort from people at every level of the BBC to deliver the savings while we continue to provide the quality programmes and services that audiences expect from us."