The bones are believed to be those of Leann Emry, but investigators can't be positive until DNA testing is done, Nyland said.
Authorities took Kimball out of a Colorado jail so he could lead them to the bodies this week, Nyland said.
Searchers in Utah found the remains on Wednesday in a remote area of eastern Utah known as the Book Cliffs.
Emry's father, Howard Emry, told 9Wants to Know previously that he has no doubt Kimball killed his daughter.
When reached Thursday after news broke, he told 9Wants to Know that authorities asked him not to speak to the media.
Leann Emry was last seen with Kimball in 2003. Her car was found abandoned that year about 18-miles from the area where her remains were found this week.
While Kimball has been in custody on theft and forgery charges in Colorado, authorities have been looking for bones and evidence in the disappearances of Kaysi McLeod, Jennifer Marcum, Kimball's uncle Terry Kimball and Leann Emry.
Only remains of McLeod, 19, who was missing for five years, have been found. Her remains were found in rural Jackson County, Colo.
Kimball has not been charged in any homicide cases.
Nyland's office learned of the possible murders about six months ago, he told The Denver Post, when the FBI called saying they had information implicating a man in killings.