Pedro Hernandez told investigators he lured Etan Patz with a soda and then strangled him while Patz on his way to school May 25, 1979, the New York Daily News reported.
New York Police Commissioner Raymond Kelly confirmed a possible suspect was in custody, the Daily News reported.
"An individual now in custody has made statements to NYPD detectives implicating himself in the disappearance and death of Etan Patz 33 years ago," Kelly said in a statement.
Hernandez had been a person of interest in the investigation before, but The New York Times reported it is unclear at what point police made him the focus of their investigation.
At the time of Patz's disappearance Hernandez worked at a bodega near where the boy was last seen.
One official told the Times Hernandez said he wrapped Patz's body in a bag and put it in a box, which he left at a building in Manhattan, and returned later to find it missing. Another official said he discarded the body.
WNBC-TV, New York, reported Patz's case had been reopened in 2010 when Manhattan District Attorney Cy Vance assumed office.
Patz's disappearance focused national attention on the issue of missing children. Shortly after he disappeared, the faces of missing children began to appear on milk cartons. Former President Ronald Reagan declared May 25 National Missing Children's Day.