Levi Aron, 37, had admitted he kidnapped and killed the boy July 11, 2011, in a trial that shook the tight-knit Hasidic Jewish community in Brooklyn.
Aron pleaded guilty to second-degree murder and second-degree kidnapping, which carry lighter sentences than if the case had gone to trial, The New York Times reported.
New York Assemblyman Dov Hikind, a representative for the Kletzky family, played down the possibility Aron could be released from prison in 40 years when he is up for parole. He said no parole board would ever let him out after considering the nature of his crime.
Leiby, who was about to celebrate his 10th birthday, disappeared on the day he was allowed to walk part of the way home from camp on his own. He apparently became lost and asked directions from Aron.
Aron said he took Leiby to a wedding in Rockland County and then returned with the boy to his apartment in Brooklyn's Kensington neighborhood. He said he became scared when he learned that police and members of the community of Hasidic Jews in Borough Park had launched a search for the boy. Aron said he smothered the child and cut up the body.
Police found body parts in a suitcase left in a trashcan more than 2 miles away and others in Aron's freezer.
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