A Vatican statement said Francis had accepted the resignations of Bishop Juan Barros of Osorno, as well as Bishop Gonzalo Duarte of Valparaiso and Bishop Cristian Caro of Puerto Montt.
Of the three, only the 61-year-old Barros is below the retirement age of 75.
Barros has been at the centre of Chile's growing scandal ever since Francis appointed him bishop of Osorno in 2015, even though he had been a lieutenant of Chile's most notorious paedophile priest, Fernando Karadima, and had been accused by victims of witnessing and ignoring their abuse.
He denies the charges, but he joined 30 of Chile's other active bishops in offering their resignations to Francis at an extraordinary Vatican summit last month.
Francis had summoned Chile's church leaders to Rome after realising he had made "grave errors in judgment" about Barros, whom he had defended strongly during his troubled visit to Chile in January.
Barros' removal, which had been expected, was met with praise by abuse survivors and Catholics in Osorno. But they warned that more resignations and actions must follow to heal the devastation wrought by the scandal.
Juan Carlos Cruz, the abuse survivor who denounced Barros for years and pressed for the Vatican to take action, tweeted: "A new day has begun in Chile's Catholic Church!
"I'm thrilled for all those who have fought to see this day. The band of delinquent bishops ... begins to disintegrate today."
Francis realised he had misjudged the Chilean situation after meeting Mr Cruz and reading the 2,300-page report compiled by two leading Vatican investigators about the depth of Chile's scandal, which has devastated the credibility of the church in a once overwhelmingly Roman Catholic country in the pope's native Latin America.
Those two investigators, Archbishop Charles Scicluna and Spanish Monsignor Jordi Bertomeu, are heading back to Chile on Tuesday to begin what the Vatican has said is a "healing" mission to Osorno.
By accepting Barros' resignation on the eve of their arrival, Francis is essentially giving Archbishop Scicluna and Monsignor Bertomeu a hand in helping to heal the divisions in a diocese where Barros was never fully accepted as bishop.
But by also accepting the resignations of the two other bishops, Francis is making clear that the troubles in Chile's church do not rest on Barros' shoulders alone, or on those of the more than 40 other priests and three other bishops trained by Fernando Karadima.
In 2011, the Vatican sentenced Karadima, a powerful preacher close to Chile's elite, to a lifetime of penance and prayer for his sex crimes.
But the Scicluna-Bertomeu report exposed a far bigger scandal that has implicated several religious orders, including priests and brothers in the Franciscans, Legion of Christ, Marist Brothers and Salesian orders.
It also exposed evidence that the Chilean hierarchy systematically covered up and minimised abuse cases, destroying evidence of sex crimes, pressuring church investigators to discredit abuse accusations and showing "grave negligence" in protecting children from paedophile priests.
Those findings, which leaked to the media while the Chilean bishops were at the Vatican, have opened a Pandora's Box of new accusations that recently led Francis to become the first pope to refer to a "culture of abuse and cover-up" in the Catholic Church.
The biggest new scandal involved revelations of a gay priest sex ring in the Rancagua diocese of the bishop who headed the Chilean church's sex abuse prevention commission. To date, 14 priests in Rancagua have been suspended and the bishop resigned as head of the commission after admitting he was slow to act on accusations that a minor had been abused.
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