Winnebago County State's Attorney Joe Bruscato agreed to drop other charges in the case, which had been set to go to trial Monday.
Neither Bruscato nor public defender David Doll commented after Thursday's hearing.
It was after Stockton's 2009 arrest in Baby Crystal's death that investigators discovered her car had been sitting in an impound lot for a year. They towed it to a Winnebago County Sheriff's Department facility to search for more clues in that case, and instead found the remains of two other infants wrapped in cloth and stuffed in separate plastic bags.
Authorities have said DNA testing found Stockton likely also was the mother of those two infants. She hasn't been charged in those deaths.
Stockton originally was questioned in Baby Crystal's death in 2004 after the newborn's frozen remains were discovered in a plastic bag along a dead-end road near her parents' home. Prosecutors said that when detectives interviewed Stockton hours after the discovery, she lifted her shirt and asked if she looked like she had just given birth.
Stockton refused to provide a DNA sample, but detectives investigating the death collected evidence from a cigarette butt they saw her discard. Authorities said saliva on the cigarette butt matched blood found on the clothing with Baby Crystal, and Stockton was arrested.
Bruscato said further tests showed Stockton was the baby's mother with a 99.96 percent certainty.
Stockton faces up to 60 years in prison when she's sentenced April 5.