Court papers say Kadish's spying took place between 1979 and 1985, although he maintained contact with an Israeli official until this year.
Kadish was arrested in New Jersey on Tuesday and was scheduled to appear before a court in New York later in the day.
US authorities also accused Kadish of illegally acting as an agent for Israel from 1979 to 2008 without notifying the US attorney-general's office.
Kadish was suspected of reporting to the same Israeli official as Jonathan Jay Pollard, who is serving a life term on a charge of spying.
Pollard, a former Pentagon official, pleaded guilty to spying for Israel in 1986 and received a life sentence.
David Mack, a former deputy assistant secretary for Near East affairs, told Al Jazeera: "I'm sure that the Israelis will say that this is based upon an old programme that they are no longer practising in any active way.
However, Mack added: "It's pretty clear from a department of justice statement that came out today, that the Israeli handler of this American army person, that the Israeli handler has been in touch with him as recently as a month or so ago."
Classified documents
The complaint alleges that the consular official, identified in the indictment as "CC-1", gave Kadish lists of classified documents to obtain from the US Army's Armament Research, Development, and Engineering Centre at the Picatinny Arsenal in New Jersey.
The documents included information about nuclear weapons, fighter jets and the US Patriot missile air defence system.
Kadish, who worked at the arsenal from 1963-1990, kept in touch with CC-1 via telephone and email and met the official in Israel in 2004, the authorities said.
"CC-1" left the US in 1985 and has never returned, the authorities said.
Arye Mekel, an Israeli foreign ministry spokesman said: "We know nothing about it. We heard it from the media."