The Pope added that he was particularly distressed by the fact that some victims of abuse had resorted to suicide.
He wrote: "These deaths weigh on my heart, on my conscience, and on that of the whole Church. To their families I offer my sentiments of love and of sorrow, and I humbly ask forgiveness."
Since his election in 2013, Pope Francis said he would take a "zero tolerance" approach against cleric abuse.
In the book, Pope Francis wrote: "How can a priest, at the service of Christ and of His Church, come to cause such evil? How can one who has consecrated his life to leading the little ones to God, end up instead devouring them in what I have called a 'diabolic sacrifice,' which destroys both the victims and the life of the Church?"
"Father, I forgive you" by Daniel Pitter will be published in Italy on Thursday.
It documents the experiences of Pitter, a Swiss man who was repeatedly raped by a friar as a boy.
Pope Francis praised Pitter for coming forward about his experiences, writing: "because testimonies such as his break down the walls of silence that stifled the scandals and the sufferings, and shed light on a terrible area of shadows in the life of the Church."