"This case cries out for a life sentence," Munsinger said.
Sigg chose not to address the judge before being sentenced and showed no emotion as the judge issued his decision. Afterward, Sigg was handcuffed and led out of the courtroom without comment.
Sigg did not face the death penalty because he was 17 at the time of Jessica's death.
His lawyers had argued state law required the judge to give him a sentence that made him eligible for parole after 40 years because he was a juvenile at the time of the crime. They cited U.S. and state Supreme Court rulings.
"Your honor, you are sentencing a child today," Defense attorney Ryan Loewer said. "Life with the possibility of parole in 40 years is the only possible and legal sentence."
Prosecutors disagreed and said the judge had the authority to hand down a longer sentence. They lauded Munsinger's decision.
"We are confident that this sentence ensures that Austin Sigg will never, ever leave the Department of Corrections and he will never, ever be in a position to prey on members of our community," District Attorney Peter Weir said.
On Monday, several of the girl's friends and family members urged the judge to impose the maximum sentence allowed.
"A part of me died that cold October day in 2012," Scott Fischle, a close friend of Jessica's family, said in arguing for a lengthy term. "She was a kind, sweet, innocent child who was bound for greatness in this world. ... My life is richer for having known her."
Jessica's mother, Sarah Ridgeway, told Munsinger the killer doesn't deserve to know how the girl's death affected her, and his name soon will be forgotten.
"Once we walk out of this courtroom we'll not remember his name and we'll only remember Jessica and the legacy she created," she said.
Defense attorneys told the judge that Sigg's mother inhaled paint while she was pregnant with him, and that trauma he suffered before and during his birth left him with head and intestinal deformities.
Jessica was abducted while walking to school Oct. 5, 2012, and human remains identified as hers were found five days later in a park. More of her remains were hidden in a crawl space in Sigg's mother's home, where he lived.
Sigg, who reportedly had a fascination with death and was interested in mortuary science, pleaded guilty to kidnapping, sexually assaulting and killing the girl. He also acknowledged attacking a 22-year-old jogger at a Westminster park in May 2012. In that case, investigators said he used homemade chloroform to try to subdue the woman, who escaped.
Jessica lived in Westminster with her mother. The fifth-grader was a member of a peewee cheerleading squad and was looking forward to being a zombie lifeguard for Halloween. Her father, Jeremiah Bryant, lives in Missouri.