Brown, who sat next to his sister-in-law in court, declined to comment as he left 4th District Judge David N. Mortensen's courtroom Thursday morning.
Steven Shapiro, Brown's attorney, said the plea was the result of nearly six months of negotiations between prosecutors and Brown.
"Today was the next step in a very long process of accountability for a reprehensible act," Shapiro said. He said the plea deal will minimize the harm a public trial would cause the family.
Shapiro said Brown was "remorseful" for what had happened.
Utah County Deputy Attorney David Sturgill said Brown's daughters consented to the plea agreement.
"They wanted their father to take responsibility, more than anything else," Sturgill said. "And they felt there should be a serious punishment."
Sturgill said the sentences are based on the guidelines that were in place at the time the crimes occurred. Under modern sentencing rules, Brown could have faced 25 years to life for the sodomy charge.
Brown's children released a statement through a spokesman Thursday evening.
"All three sisters are at peace with the agreement that has been reached in this case," the statement reads. "While, clearly, the current events surrounding the family are painful, the sisters were well prepared for this day and are relieved and grateful to close this chapter in their lives."
On Wednesday, the group's three adult sisters publicly revealed that their father sexually abused them as children.
"We can confirm that Keith Brown has been charged with sexual abuse involving his daughters," wrote Kimball Thomson, a spokesman for The 5 Browns, in a statement.
The Salt Lake Tribune generally doesn't name victims of sexual abuse, but in this case, Thomson said the sisters Desirae, 32, Deondra, 30, and Melody, 26 consented to the release of their identities.
Sturgill said Brown engaged in sexual activity with one of his daughters, who, at the time, was under the age of 14, between November 1990 and October 1992.
During that same time period, Brown also fondled another daughter when she was under the age of 14, and he repeated the offense between March 1997 and March 1998.
A source close to the family told The Tribune that the sisters called police after recently learning their father, who managed the quintet until 2008, planned to again manage child musicians.
"The case, brought by the Utah County Attorney's Office, was initiated by the three Brown sisters," Thursday's statement from the Browns reads. "The women were motivated to approach law enforcement out of concern for the welfare and protection of other young women and girls."
Sturgill said the Utah County Attorney's Office was approached in late summer, and negotiations began on the plea agreement Brown entered into Thursday.
Brown is free pending his sentencing.
"I don't think he's a risk to anyone right now," Sturgill said.
News of the charges came earlier this week after a single-car crash involving Brown and his wife, Lisa.
The couple were hospitalized after the Porsche that Brown was driving plummeted 300 feet down a Little Cottonwood Canyon embankment and into a creek Monday night.
Police have said Brown, who was driving his wife back from a Valentine's Day dinner at Snowbird Ski and Summer Resort, was driving too fast.
Shapiro said there was no evidence that the accident was a suicide attempt.
"The information I have was that there was, in fact, an accident, and it perhaps involved driving faster than conditions allowed," Shapiro said.