The 42-year-old will be committed to a state mental hospital, with periodic hearings before a judge to determine whether she should be released. If convicted of murder, she would have faced life in prison.
Yates' attorneys never disputed that she drowned 6-month-old Mary, 2-year-old Luke, 3-year-old Paul, 5-year-old John and 7-year-old Noah in their Houston-area home in June 2001. But they said she suffered from severe postpartum psychosis and, in a delusional state, believed Satan was inside her and was trying to save them from hell.
Yates stared straight ahead, stoically, as the verdict was read, CBS News correspondent Steve Futterman reported. She then bowed her head and wept quietly.
The children's father, Rusty Yates, said outside court that the jury had reached the right conclusion.
"Yes, Andrea took the lives of our children, that's the truth, but also yes, she was insane," Rusty Yates said. He divorced Andrea Yates after the children's June 2001 deaths and has supported his former wife since, CBS News correspondent Lee Cowen has reported. Rusty said they are still "friends" and reminisce about the children.
The jury, split evenly among men and women, deliberated for about 12 hours over three days before finding Yates not guilty by reason of insanity. The jurors had not been told that she would be committed to a mental institution for treatment if found not guilty.
"I'm very disappointed," prosecutor Kaylynn Williford said. "For five years, we've tried to seek justice for these children."
Yates' lead defense lawyer, George Parnham, called the verdict a "watershed event in the treatment of mental illness."
Prosecutors had maintained that Yates failed to meet the state's definition of insanity: that a severe mental illness prevents someone who is committing a crime from knowing that it is wrong.
"No one should believe that she is getting off easy. She's going to be committed to mental health facility, probably for the rest of her life. And every time her medicine allows her to regain a little bit of sanity, she realizes what she did to her beloved children and then descends again into some sort of madness," CBS News legal correspondent Andrew Cohen said. "So this started as a tragedy and continues even with this verdict."
An earlier jury had found Yates guilty of murder in her children's deaths, but that verdict was overturned on appeal because erroneous testimony. Prosecutors retried her on the same three counts of murder.
In both trials, Yates, 42, pleaded innocent by reason of insanity. Under Texas law, a person can be found insane if, because of a severe mental illness, he or she does not know the crime is wrong.
The jury earlier asked to review the videotape of Yates' July 2001 evaluation by Dr. Phillip Resnick, a forensic psychiatrist who testified for the defense that she did not know killing the children was wrong because she was trying to save them from hell.
Resnick told jurors that Yates was in a delusional state and believed her children would grow up to be criminals because she had ruined them.
Jurors later asked to review Yates' November 2001 videotaped evaluation by Dr. Park Dietz, the state's expert witness whose testimony led an appeals court to overturn Yates' 2002 capital murder conviction last year.
Dietz, a forensic psychiatrist, testified in her first trial that an episode of the television series "Law & Order" depicted a woman who was acquitted by reason of insanity after drowning her children. But no such episode existed. State District Judge Belinda Hill barred attorneys in this trial from mentioning that issue.
On Tuesday, after jurors asked for the trial transcript involving defense attorney George Parnham's questioning of Dietz about the definition of obsessions, the judge brought the jury back into the courtroom.
The court reporter then read the brief transcript, in which Dietz said Yates "believed that Satan was at least present. She felt or sensed the presence." Dietz had testified that Yates' thoughts about harming her children were an obsession and a symptom of severe depression, not psychosis.
Mental health experts say that the Yates case has focused long-overdue attention on the issue of post-partum depression and psychosis, both poorly-understood phenomena that they say should be treated, not punished, CBS News correspondent Elizabeth Kaledin reports.
"This case illustrates in the most tragic fashion the consequence of untreated or under-treated mental illness," says Dr. Shari Lusskin of the NYU School of Medicine.
Earlier Tuesday, jurors reviewed the slide presentation of the state's key expert witness, Dr. Michael Welner, a forensic psychiatrist who evaluated Yates in May. He testified that she did not kill her children to save them from hell as she claims, but because she was overwhelmed and felt inadequate as a mother.