All the alleged abuse involves former priest Michael Baker, and the cases span 26 years from 1974 to 2000.
"The archdiocese has accepted full responsibility for the misconduct of Michael Baker," said J. Michael Hennigan, attorney for the L.A. archdiocese. "With respect to his victims, it is simply a matter of reaching an agreement with a reasonable settlement. We are always pleased to resolve these cases. We are nearly done."
Two cases were to go to trial next month. A judge had said he would allow punitive damages at trial.
Recently released files show Baker confessed to Cardinal Roger Mahony in 1986 that he molested two brothers for nearly seven years. Mahony sent Baker to psychological treatment and assigned him to a ministry where he molested again. Baker was convicted of molesting a boy in 2007 and paroled in 2011.
Mahony, who is currently in Rome helping select the next pope, is aware of the settlement, Hennigan said. The former Los Angeles archbishop has been criticized for not doing enough to stop the abuse and was rebuked by his successor, Archbishop Jose Gomez, last month after clergy abuse files showed Mahony tried to protect the church from scandal rather than protect the children.
Two of the plaintiffs, a pair of brothers, will get $4 million each, and the two others will get nearly $1 million each. The archdiocese settled more than 500 clergy abuse lawsuits in 2007 for a record-breaking $660 million.
The Associated Press contributed to this report.