The scheme was the idea of Cardiff schoolgirl, Natalie Vaughan, 12, and is set to create 30 hectares (74 acres) of broad-leaved woodland annually.
First Minister Rhodri Morgan will plant a tree in Monmouthshire later and said the initiative would also "help connect young people" with nature.
Approximately 35,000 children are born or adopted in Wales each year.
From New Year's Day, each new-born baby or newly-adopted child will receive a certificate stating that a tree has been planted for them.
'A win-win'
The project, called Plant!, was the idea of the pupil Llanishen High School in Cardiff, when she was 11.
She suggested it would be a good way to make young people think about their environment and the role they have in preserving it.
Natalie was due to join Mr Morgan at the Woodland Trust site, Cefn Ila, near Usk, to plant a tree with the help of pupils from Ysgol Llanfair Kilgeddin, Abergavenny.
Parents will receive a certificate and will also be able to find out where the tree has been planted
Plant! is expected to boost the assembly government's aim of creating a national forest of native trees, to act as a carbon sink to help tackle climate change.
Forests and woodland cover about 13.7% of Wales. The assembly government owns 38% of Welsh woodlands. They are managed by Forestry Commission Wales.
The Plant! scheme is being run by Coed Cadw (Woodland Trust) and Forestry Commission Wales.
Mr Morgan said: "This scheme is a win-win for us all, as it not only contributes to regenerate our native woodlands but also links children with the natural environment.
"As they grow older, they will be able to follow the progress of the site of their very own tree and appreciate the importance of protecting and supporting our native species of plant and wildlife."
Jerry Langford of the Woodland Trust added: ?The symbolism of planting a tree to mark a child?s birth marks the beginning of their life with a positive environmental action."