Leaders are pledging to work with Professor Alexis Jay and the Independent Inquiry into Child Sexual Abuse (IICSA) in a "constructive and transparent manner".
Bishop of Bath and Wells, Peter Hancock, the CofE's lead bishop on safeguarding, said: "We welcome the news ...of the appointment of Professor Alexis Jay as the new chair of the Independent Inquiry into Child Sexual Abuse (IICSA) and her public commitment to continue the important work it has done so far in hearing the voices of survivors and looking at institutional failings.
"The Archbishop of Canterbury requested that the Church be one of the first institutions to be considered in the work of the inquiry and we will continue to work in a constructive and transparent manner with IICSA under Professor Jay's leadership."
Home secretary Amber Rudd announced on Thursday that Professor Jay, who already sat on the Inquiry's panel, will take over as chair, following the resignation of Dame Lowell Goddard last week.
Launched two years ago, the investigation is looking at how the CofE and the Roman Catholic Church, among other institutions in England and Wales, have dealt with abuse.
Professor Jay becomes the fourth person to chair the Inquiry.
David Pearson from the Churches Child Protection Advisory Service (CCPAS) told Premier Christian Radio Professor Jay's appointment should mean a smoother transition for the Inquiry.
He said: "It means that the work will continue and I think this will be welcomed by victims and survivors, who I feel would have feared there could have been some ground lost here."
Professor Jay previously led an inquiry which revealed at least 1,400 children were subjected to sexual exploitation in Rotherham.
Speaking with Premier Christian Radio, Christian lawyer from the Stop Church Child Abuse, campaign David Greenwood also expressed his confidence in Professor Jay.
He said: "She has lots of experience in this field, is well-used to writing reports and I perceive her to be a team player and someone everyone will work around."
Click here to listen to David Pearson from CCPAS.