Tuesday's decision by Judge Judith Atherton will send Brian David Mitchell to a state hospital until he is deemed capable of standing trial.
The judge issued her decision after six days of hearings over the past seven months. Mitchell repeatedly shouted Biblical admonitions and sang hymns during the hearings, prompting him to be removed from court several times.
Last year the judge ruled Mitchell's wife, Wanda Barzee, was not competent to stand trial either.
In her decision the judge noted that testimony showed Mitchell's family had a history of mental disorder. Mitchell was the third of six children and a "loner" in a "highly dysfunctional" family, the judge wrote.
Prosecutors argued that Mitchell was simply a narcissist with an extreme set of religious beliefs.
Elizabeth's father, Ed Smart, said he was resigned to the judge's decision about the family's one-time handyman.
"My satisfaction will be seeing him behind bars, not back out on the street to hurt anyone again," Ed Smart said. "If he wants to be the way he is, so be it, and let him waste away in a mental hospital."
Mitchell, 51, is accused of kidnapping then 14-year-old Elizabeth from her bedroom in 2002, sexually assaulting her and keeping her as his second wife.
Mitchell and Barzee, 59, were charged with kidnapping, aggravated sexual assault, aggravated burglary and attempted aggravated kidnapping. He also was charged in the attempted abduction of Elizabeth's cousin. Barzee has filed for divorce.
Prosecutors expressed optimism that Mitchell would eventually be found competent to stand trial.
"We anticipate there will be a trial someday, and Elizabeth will testify and he will be convicted," District Attorney David Yocom said.
Mitchell's chief public defender, Vernice S. Trease, did not respond immediately to phone messages Tuesday.
Under Utah law, Mitchell will return to court in three months to determine whether his mental state has changed, a prosecutor said.