The British-born Kimche began his career with Israel's Mossad spy agency in the 1950s after emigrating to Israel, and rose to deputy director of the agency. He later served as director-general of Israel's Foreign Ministry.

In the Iran-contra affair, Washington authorized Israel to sell US weapons to Iran in violation of an international embargo. Some of the proceeds later went to fund anti-communist Contra rebels in Nicaragua.

Israeli Prime Minister Benjamin Netanyahu praised Kimche for the way he “combined elegance, patriotism and sophistication” and “exemplified how to fulfill a public mission.”