Recently released files show Cardinal Roger Mahony knew the priest had abused but put him back into ministry, where he is alleged to have abused again.
The settlement comes as the cardinals of the Catholic Church are meeting to select a new pope following the abdication of Benedict XVI.
Cardinal Mahony is at the conclave.
Nearly 10,000 US Catholics signed a petition urging him not to go because of the allegations he protected priests accused of child sex abuse.Church files
Cardinal Mahony was the popular archbishop of the Los Angeles Archdiocese - the largest in the US, representing five million Catholics - for 26 years until his retirement in 2011.
As part of this settlement, no parties admit any wrongdoing.
But thousands of pages of church files were recently released on a court order, revealing that Cardinal Mahony shielded a number of accused priests from the law; among them Baker, who in 1986 was sent for psychological treatment at a church-run centre and then allowed back into ministry.
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The person who could have stopped this in its tracks... is now sitting in Rome voting for the next vicar of Christ. I find that terribly troubling”John ManlyPlaintiff's attorney
He went on to abuse again and this payment of $9.9m relates to four of his alleged victims, who accused him of molesting them - and claimed the cardinal covered up his behaviour.
Two of the plaintiffs, who are brothers, will get $4 million each, and the two others will get nearly $1 million each, plaintiff's attorney John Manly said according to the Associated Press news agency.
Baker was convicted of child molestation in 2007 - the same year the LA archdiocese reached a record-breaking $660m settlement with hundreds of abuse victims - and released in 2011.'Mistakes'
This is a further embarrassment for the archdiocese and especially for Cardinal Roger Mahony, says the BBC's Jane Little in Washington.
Cardinal Mahony has called Michael Baker his "greatest mistake".
"We have for a long, long time said that we made serious mistakes with Michael Baker and we had always taken the position in these cases that whatever Baker did we were responsible for,'' AP quoted J Michael Hennigan, an archdiocese attorney, as saying.
"That was never an issue.''
"The person who could have stopped this in its tracks and prevented three out of four of these children from being sexually assaulted is now sitting in Rome voting for the next vicar of Christ,'' said Mr Manly.
"I find that terribly troubling.''
