The helpline charity officially became part of the NSPCC last week in order to secure its long-term future. It had been battling financial problems for more than a year.
ChildLine will retain its name, logo and helpline number, which are already on the NSPCC's website. Easton will stay on to oversee the transition, but she will not have a role within the amalgamated organisation.
The same volunteers will take calls at the helpline, whose managers will also be transferred. ChildLine founder Esther Rantzen and one other ChildLine trustee will sit on the 16-strong NSPCC board.
ChildLine currently has 230 employees. The NSPCC has said there will be an immediate recruitment freeze at both organisations.
Easton said: "The NSPCC is committed to avoiding compulsory redundancies wherever possible. But there can't be two chief executives. We are in discussions with directors and, where there is a duplication of roles, there might be a small number of redundancies."
Mary Marsh, chief executive of the NSPCC, said it was too early to say what would happen to ChildLine's regional offices.
"We understand that any relocations should not be done in a hurry," she said. "ChildLine needs to be distributed in a way that will give it access to a wide pool of volunteers. We aim to keep things intact, but we will need to keep it under review."
See News Analysis, page 10, and Editorial, page 22.