Acknowledging that bishops can already be removed from office for "grave causes", the pontiff has taken the measure of specifying that this includes "the negligence of a bishop in the exercise of his role, especially in relation to cases of sexual abuse of minors and vulnerable adults", the Vatican has said.
A number of sex abuse scandels involving the Roman Catholic Church in recent years have included allegations priests have been transferred to different areas instead of being reported to police.
Let us hear the cry of the victims and those suffering, no family without a home, no child without a childhood.— Pope Francis (@Pontifex) June 4, 2016
Commenting on the Motu Proprio letter written by Pope Francis, the Holy See added a bishop: "may legitimately be removed from office for acts committed or omitted by negligence, resulting in the provocation of grave damage to others, either physical persons or a community as a whole.
"The damage may be physical, moral, spiritual or patrimonial. The diocesan bishop or eparch may be removed from office only if he may be shown objectively to have lacked the diligence required for his pastoral office, even without grave moral culpability on his part.
"In the case of abuse of minors or vulnerable adults, it is sufficient for the lack of diligence to be grave."
It has also emerged a new "college of legal experts" - expected to consist of cardinals and bishops - will help the pontiff reach a decision when judging accusations of negligence in such cases.
The announcement has been slammed by David Clohessy, director of the US-based abuse survivors group, Survivors Network of those Abused by Priests (SNAP).
Mr Clohessy said: "A 'process' isn't needed. Discipline is what's needed. A 'process' doesn't protect kids. Action protects kids.
"A 'process' is helpful only if it's used often enough to deter wrongdoing. We doubt this one will be."
The Motu Proprio, released at the weekend, will come into effect from 5 September 2016.