The 36-year-old Aron admitted killing the child after the boy asked him for directions.
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Aron's attorney, Jennifer L. McCann, said she was "glad we were able to come up with an amenable resolution that both sides agreed to."
"I know this has been a very difficult case for all of Brooklyn, and I appreciate the patience," she said.
"In these kinds of cases, people have rights. And we had to make sure to do our do diligence in resolving the case."
Police say Leiby's dismembered body was found in Aron's freezer and inside a suitcase in a nearby trash bin.
New York City's chief medical examiner said the Brooklyn boy died last summer after being drugged and then smothered.
The autopsy results for Leiby listed a cocktail of four prescription and over-the-counter drugs in the boy's system: cyclobenzaprine, a muscle relaxant; quetiapine, an antipsychotic drug; hydrocodone, a pain medication; and acetaminophen, the drug found in Tylenol.
The boy traces of a muscle relaxant, cyclobenzaprine; an anti-psychotic drug, quetiapine; pain medication and Tylenol in his blood, an autopsy showed.
In a written confession to police, Aron admitted smothering Leiby with a towel before dismembering the boy's body.
Both Aron and Leiby were members of the borough's close-knit Orthodox Jewish community, although police say it doesn't appear that they knew each other.
Kletzky's family released a statement through New York Assemblyman Dov Hikind's office, saying they have "finally received some partial closure on one aspect of this nightmare."
"There is no way one can comprehend or understand the pain of losing a child," said Nachman and Esther Kletzky in the statement.
"Closure does not mean we don't continue to feel the pain. A day doesn't pass without our thinking of Leiby -- but today we close the door on this one aspect of our tragedy and seek to remember only the gifts that G-d has bestowed."
Leiby disappeared on Monday, July 11 after apparently getting lost the very first time his parents let him walk home from school by himself.
The boy had just left a day camp in Brooklyn's Orthodox Jewish Borough Park neighborhood.
The boy's parents had agreed to let him walk by himself seven blocks from camp to a meeting point halfway home, said New York Police Commissioner Ray Kelly.
But he never arrived.
READ TRANSCRIPT OF ARON"S CONFESSION TO POLICE
Surveillance tapes show the boy encountering Aron outside a dentist's office, where police determined Aron had just paid a bill.
Leiby seemed to have lost his way and asked Aron, a stranger he met on the street, for directions, Kelly said.
The boy's dismembered body was found two days later.
Part of the remains were found in Aron's freezer.
The rest of the body was found inside a red suitcase that had been tossed into a trash bin in another Brooklyn neighborhood, Kelly said.
Aron, a former butcher and clerk at the Empire State Supply Co. hardware store on McDonald Avenue in Kensington, allegedly suffocated the boy with a towel after giving him a tuna sandwich.