The men alleged they were abused by former priest Michael Baker, who authorities suspect molested 23 boys over three decades, the Los Angeles Times reported Tuesday.
The newspaper noted the archdiocese has settled other cases involving Baker but this was the first one since it released 12,000 pages of internal records about abuse by members of the clergy in January.
Plaintiff's attorney John Manly said two brothers will receive $4 million each, and the other two men will get nearly $1 million apiece, USA Today reported.
Baker, since defrocked, was convicted in 2007 of child molestation and has been on parole since 2011, USA Today said.
The Times said the settlement came as two of the civil suits were to go to trial next month. Another plaintiff's attorney, Vince Finaldi, said he believed the release of the thousands of pages of documents, including Cardinal Roger Mahony's involvement in the church's handling of Baker, "played heavily" into the archdiocese's decision to settle.
"Once we got the files, it confirmed everything we had argued for years and years," Finaldi said. "Cardinal Mahony's fingerprints were all over the case."