Police said Sigg had confessed to the crime and that officers discovered of some of the girl's remains at his home.
The plea came two days before Sigg was set to stand trial and nearly a year after the girl's disappearance set communities on edge. Lawyers and court officials previously declined to release details of the plea, citing a gag order in the case.
Jessica left home to walk to school in Westminster on Oct. 5, 2012, but never arrived.
Hundreds of people helped search for Jessica and two days later her backpack was found in Superior, a town about 6 miles away from her home.
A few days later, human remains later identified as Jessica's were later found in a park and police announced that Jessica's parents — Sarah Ridgeway of Westminster and Jeremiah Bryant of Missouri —weren't under suspicion and they were looking for an "unknown suspect."
They told residents that the abductor was probably someone they knew and urged them to be watchful for any suspicious changes in behavior. Officers guarded crosswalks and photographed cars in the area. Mailboxes and trees were encircled by ribbons in Jessica's favorite color, purple.
Sigg was arrested after his mother called police. She said he turned himself in.
Sigg dropped out of high school after 11th grade and later earned a GED. Former classmates say he was intelligent but complained about school and was bullied for having a high voice.
At Jessica's memorial service, Pastor Rick Long of Grace Church said she loved Disney films, was a member of the peewee cheerleading squad at a nearby high school, and had been looking forward to dressing up as a zombie lifeguard for Halloween.