It said in a statement that Arye Eliyahu "Eli" Cohen should be rendered to US authorities "in order to stand trial for the commission of federal offences of trading military spare parts with Iran".
"According to the charge sheet on which the extradition request is based, during the years 2000-2004 Cohen exported military spare parts from the United States to his place of residence in Israel," the Hebrew-language statement said.
It said that he and three accomplices in the United States shipped parts for Hawk missiles, fighter aircraft and armoured troop carriers from the US to Israel, using false declarations as to the materials and their final destination.
The charges were filed in the Federal District Court of Connecticut in 2013, and the United States made an extradition request the following year.
The Jerusalem District Court granted the request but Cohen then appealed to the Supreme Court.
"The act for which extradition is requested constitutes a criminal offence under the laws of both" Israel and the United States, the court said in today's ruling.
Prime Minister Benjamin Netanyahu has accused arch-foe Iran of "preparing another Holocaust" and seeking to acquire nuclear arms with which to attack the Jewish state.
An arms embargo on the Islamic republic remains in force.
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