Justin Welby said an abuse inquiry would probably find "bad stories" about the Church.
The Home Office has announced an inquiry into allegations of historical child abuse in public institutions in the 1970s, 1980s and 1990s.
The Most Rev Justin Welby told the BBC's Andrew Marr Show he is dealing with allegations of child sex abuse within the church every day.
"It is becoming clearer and clearer that for many, many years things were not dealt with as they should have been dealt with." He said.
The Archbishop also said the Church would have to apologise for the "terrible things" in its past.
The inquiry was confirmed by Home Secretary Theresa May who told MP's: "Our priority must be the prosecution of the people behind these disgusting crimes.
"That wherever possible, and consistent with the need to prosecute, we will adopt a presumption of maximum transparency.
"And that where there has been a failure to protect children from abuse, we will expose it and we will learn from it."
The abuse inquiry will be led by Baroness Butler-Sloss. She's faced accusations she's not the right person for the job.
In a previous investigation into abuse in the church she was accused of telling an abused choir boy she wanted to exclude some of his claims from her report so she could protect the Church of England.
Baroness Butler-Sloss said she has never put an organisation in front of a victim.
The Home Office has pledged its full support for her saying she had its "unreserved" backing.