Plant! was announced last February as part of the Welsh Assembly Government's drive for a more sustainable environment.
About 35,000 children are born or adopted in Wales every year and it is hoped up to 30ha of new woodland will be planted annually to create a Welsh National Forest of native trees.
A certificate will be sent to each family telling them where their child's tree is planted and how they can visit it.
Woodland Trust Wales director Jerry Langford said: "The symbolism of planting a tree to mark a child's birth marks the beginning of their life with a positive environmental action. It will inspire further positive steps by all families involved in the project."
The scheme has been set up on behalf of the Welsh Assembly Government by the Woodland Trust and Forestry Commission Wales.
Community and school planting events will be organised locally to help raise awareness for the project and its aims.