Moshe Arens was born in Kaunas, Lithuania, to a Jewish family. His father was an industrialist and his mother was a dentist. When he was a year old, his family moved to Riga, Latvia. where he attended elementary school. In 1939, Arens and his family immigrated to the United States, where his father had business interests. The family settled in New York City, where Arens attended George Washington High School. As a youth, Arens was a leader in in the Betar youth movement. During World War II, Arens served in the United States Army Corps of Engineers as a technical sergeant. Following the Israeli Declaration of Independence in 1948, Arens moved to the new State of Israel and joined the Irgun, despite the opposition of his father. He was sent to North Africa (mostly Morocco and Algeria) and Europe to help local Jewish communities establish self-defense groups. In March 1949, he returned to Israel, and became a founding member of the Herut party, which had grown out of the Irgun. After being denied a job in Israel's military industries, he began working as an engineer for an American company dealing in designing water systems for Tel Aviv. In 1951, he returned to the United States, and studied engineering at the Massachusetts Institute of Technology and aeronautical engineering at the California Institute of Technology where he was a student of Qian Xuesen, then worked for a time in the aircraft industry. He returned to Israel in 1957, and became professor of aeronautics at the Technion, serving in this position until 1962. From 1962 until 1971 he was a Deputy Director General at Israel Aircraft Industries, where he was in charge of most major development projects, including the Kfir fighter jet project. In 1971, he won the Israel Defense Prize.
He was re-elected in 1984, but was only appointed Minister without Portfolio. After another re-election in 1988 he was appointed Minister of Foreign Affairs (with Netanyahu his deputy), and in 1990 returned to the Defense portfolio.
After Likud lost the 1992 elections, Arens retired from politics. However, he returned in 1999 to challenge Binyamin Netanyahu for the Likud leadership. Although he failed in his challenge, winning only 18% of the vote, Netanyahu appointed him Minister of Defense, replacing Yitzhak Mordechai, who had left Likud to establish the Centre Party.
Although Arens returned to the Knesset after the 1999 elections, Likud lost the elections and he left the cabinet. He lost his seat for the final time in 2003.
While living in the United States, Arens married Muriel F. Eisenberg from New York, and she moved to Israel with him. The couple had four children; Yigal, Aliza, Ranan, and Rut.
Since retiring from the government, he has also devoted considerable efforts to researching and commemorating the story of the Jewish Military Union (ŻZW), which fought alongside the better known Jewish Combat Organization (ŻOB) in the Warsaw Ghetto Uprising.
A prolific hobby historian, Arens is the author of a number of articles on the revolt as well as a popularly acclaimed book, Flags over the Warsaw Ghetto, which appeared in Hebrew, Polish and English.