According to Wikipedia:

Having been exported to Pahlavi Iran under the Western-aligned Shah Mohammad Reza Pahlavi in 1976, F-14s were used as land-based interceptors by the Imperial Iranian Air Force. Following the Iranian Revolution in 1979, the Islamic Republic of Iran Air Force used them during the Iran–Iraq War.

https://en.m.wikipedia.org/wiki/Grumman_F-14_Tomcat

Iran was Western-aligned during the Cold War. When the Shah's authoritarian regime was overthrown in 1979, Iran kept the military hardware that the US supplied the Shah with.

Follow up question: How did they keep the buggers running without OEM parts for nearly 50 years?