Eric Bellucci, who was arrested at Tel Aviv airport on Friday, was in custody of New York City police, said William Smith, a spokesman for the Staten Island district attorney.
Bellucci's parents, Arthur, 61, and Marian, 56, were found dead Wednesday night in their Staten Island home.
Bellucci was picked up Friday after trying to buy a plane ticket to Beijing. His confused manner alerted a flight clerk who notified security officials.
Bellucci is not an Israeli citizen, and it was unclear why he had traveled to Israel.
Israeli authorities said they had been searching for Bellucci for nearly 24 hours in coordination with the New York Police Department before his arrest.
Footage broadcast on Israeli TV showed police hauling an unshaven, woozy Bellucci from the airport into a van. His eyes were shut and he did not resist.
Liron Cohen, an airport check-in attendant, told Israel's Channel 10 on Friday that the man "appeared unstable, spoke to himself and wasn't sure what he wanted" when he was at her counter.
He tried to buy a one-way ticket on a Turkish airline to Beijing via Istanbul, but his credit card was rejected, she said. When he offered to return with cash, she checked his passport, called her supervisors and security detained him, she said.
The NYPD said it found Bellucci's parents Wednesday night after a 911 call from a relative. The New York Post reported that the couple's daughter had found their bodies.
Police found Bellucci's SUV parked at Newark Liberty International Airport in New Jersey.
The NYPD said previously that the son lived with his parents and suffered from schizophrenia.
He was once a star athlete at Stuyvesant High School in Manhattan, and his father was a senior associate at a large real estate company, according to published reports.