Kimball, who committed the murders while working as an FBI informant, pleaded guilty in 2009 to killing Kaysi McLeod, 19; Jennifer Marcum, 25; LeAnn Emry, 24; and his uncle, Terry Kimball, 60, between January 2003 and August 2004.
Despite his guilty pleas, he'd maintained that other people were present and that, in two cases, they fired the shots that killed the victims.
A summary document of his 147-page letter was obtained by the Daily Camera of Boulder. A law enforcement source with knowledge of the investigation confirmed its authenticity, the newspaper said.
The FBI is reviewing the letter and may interview Kimball about the crimes.
Ed Coet, Kimball's cousin and the author of a book about his crimes, said Kimball is confessing because he is concerned about his soul's salvation.
"Scott does not want to go to hell when he dies," Coet told the newspaper.