The entire Chilean delegation of bishops tendered its resignation to the pope last month after a series of meetings at the Vatican.
The mass resignation of an entire delegation of bishops is almost unheard of, having last happened two centuries ago.
Several members of the Chilean church hierarchy are accused by victims of ignoring and covering up child abuse by Chilean paedophile priest Fernando Karadima during the 1980s and 1990s.
The scandal is the latest to rock the Roman Catholic Church, and Argentine-born Francis has said it must not happen again on his watch.
But the pontiff himself became mired in the scandal when, during a trip to Chile in January, he defended Barros who was accused of covering up Karadima's wrongdoing.
Karadima was suspended for life by the Vatican over the allegations of child molestation.
The announcement of Pope Francis's decision to accept the resignation was made in a Vatican statement which named the other two bishops as Cristian Caro Cordero and Gonzalo Duarte García de Cortázar.
Pope Francis has apologised to the victims and admitted he had made "grave mistakes" after reading a 2,300-page report on abuses in Chile.
In a letter to Chileans released at the end of last month, the pontiff voiced "shame" that the Catholic church failed "to listen and react in time" to the allegations of sexual abuse by Chilean clergy.
He has since received two groups of Karadima's victims at the Vatican.
Since 2000, about 80 Roman Catholic priests have been reported to authorities in Chile for alleged sexual abuse.
In 2015, Francis appointed Barros as the head of the southern diocese of Osorno despite accusations he had covered up for Karadima.
'I was part of the problem'
Last month Francis promised "changes" to the Chilean church to "restore justice" in a short declaration to the bishops that was made public.
The letter -- handed to the bishops at the start of their meetings with Francis -- evokes "crimes" and "painful and shameful sexual abuse of minors, abuses of power and conscience by ministers of the Church".
It qualifies the removal of certain prelates from their roles as necessary but "insufficient," calling for "the roots" that allowed for such abuse within an "elitist and authoritarian" Chilean Church to be examined.
One of Karadima's victims whom the pope hosted at his Vatican residence and met individually said the pontiff was "contrite" and said he had been "part of the problem".
"I told him that Barros was watching us when we were abused, I think that's clear to him now," Juan Carlos Cruz said.
"He (the pope) said, 'I was part of the problem, I caused this'," Cruz added.
Some of the victims have accused Cardinal Francisco Javier Errazuriz, a key advisor to Francis, of ignoring and helping to cover up Karadima's abuses.
Despite a strong Catholic tradition, Chile is witnessing a growing rift between the people and the Church, sharpened by the string of sexual abuse scandals.
President Sebastian Pinera, a practising Catholic, recently said he was saddened by the fact that the Church "is increasingly remote, not only from worshippers but from people in general."
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