Mortensen called Brown a pedophile and a "danger to society," but said he was being given a lighter sentence "through the consent of your victims."
Under current sentencing guidelines, Brown would have faced a term of 25 years to life.
Brown's children were the first sibling quintet to study at the famed Julliard School in New York City.
The 5 Browns, made up of Brown's two sons and three daughters, went on to produce successful classical-music albums and make appearances on "The Oprah Winfrey Show" and "60 Minutes."
When Brown's daughters recently learned their father planned to mentor other children in musical careers, they reported the abuse to authorities.
After six months of discussions and negotiations, Brown was charged in February with one first-degree felony count of sodomy on a child and two second-degree felony counts of sexual abuse of a child.
The charges stem from three instances in the 1990s, but Mortensen said the state's Board of Pardons and Parole should consider the fact that there "could have been many more charges."
Deputy Utah County Attorney David Sturgill said Brown's daughters were abused for years and that it "has changed the course of their lives."
"This is what the victims wanted," Sturgill said of the sentence. "I hope they're happy [with the resolution]."
The Salt Lake Tribune generally doesn't name victims of sexual abuse, but a spokesman for the family said the sisters Desirae, 32, Deondra, 30, and Melody, 26 consented to the release of their identities.
The same spokesman said the family wouldn't comment on Thursday's sentencing.
Brown said nothing on his behalf in the Provo courtroom.
His attorney said he submitted a written statement as part of a presentencing report, which isn't a public record.
"I think he's remorseful, and I think every step he's taken in the process ... has been geared toward taking responsibility," Steve Shapiro added.