The Vatican tribunal section will be responsible for looking into cases where a bishop is accused of covering up for a paedophile priest or encouraging a victim to stay silent.
To date no bishop has ever been removed for protecting abusive clergy but in April the pontiff accepted the resignation of a US bishop who had been convicted by a court of not reporting a suspected sex offender.
The tribunal is widely seen as the Vatican's biggest step yet to hold bishops accountable in sex abuse cases.
Cardinal Seán Patrick O'Malley, who's been looking into how the church deals with abuse, made the suggestion in a report to Francis.
In a statement the Vatican said: "The Holy Father approved the proposals and authorised that sufficient resources will be provided for this purpose."
The Churches' Child Protection Advisory Service welcomed the move.
Simon Bass, CEO, said: "Pope Francis has also established a five year period within which these proposals are to be developed and evaluated.
"We say that the success of the Tribunal should be judged according to one simple criterion: since Bishops who cover up abuse should be removed from office immediately, how many will no longer be in post, for this reason, at the end of those five years?
"Only by ending what the Vatican has itself termed the 'Abuse of Office' by Bishops can children in the Church ever really be safe.
"The establishment of the Tribunal has implications far beyond the Roman Catholic church, too.
"CCPAS has for some time been calling for mandatory reporting for those in positions of authority in the UK (such as ministers of religion) to report to the police all instances of child sex abuse in the UK as soon as they come to light.
"The same principles must apply to every other Christian denomination and every other faith group immediately. We continue to call on the government to introduce mandatory reporting in the UK as quickly as possible."