Hamilton County Chief Deputy Prosecutor Andre Miksha said in a statement that "no one is really happy" with the plea agreement.
Prosecutors said Harrison stabbed his son, Michael, in the chest with a kitchen knife and in the forehead with a nail-pulling tool at his parents' Noblesville apartment in January 2013. Harrison was 30 at the time.
Harrison had originally sought an insanity defense, but prosecutors argued that one of three mental health specialists who examined him concluded that he wasn't insane at the time of the killing but was under the influence of drugs. Miksha said Harrison had a history of drug use and killed his son at the end of a weekend methamphetamine bender.
Two other specialists said they believed Harrison was schizophrenic and was insane at the time of the killing.
Miksha said under the plea agreement, Harrison gave up his opportunity to be found not guilty by reason of insanity and that the state surrendered its chance to seek a sentence of life without parole.
Harrison begged the judge to kill him at his initial hearing in January 2013.
The boy's mother said Harrison took Michael and two daughters without her permission.
Police found the toddler with two knife-stab wounds to his chest and one wound in the forehead.
The boy's grandmother, Pamela Harrison, told officers that "Micah stated that someone or something was trying to kill him" and that he hit a closet with a hammer, which she took from him, telling the man no one was there.
After she hid the hammer in a bedroom, a police affidavit said, she saw her son "moving quickly from the kitchen to the other bedroom where she knew Michael was playing." She said she found her son atop the boy, who was lying on the floor, and watched him stab Michael with the knife.
The other children weren't harmed.
Since his arrest, Harrison has been held at the Hamilton County Jail in Noblesville, about 20 miles north of Indianapolis.