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 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.
While living in the United States, Arens married Muriel F. Eisenberg from New York City, and she moved to Israel with him. The couple had four children, two boys and two girls; Yigal, Aliza, Raanan, and Rut. Arens is chairman of the International Board of Governors of the Ariel University Center of Samaria and writes for Haaretz.
In 1971, Arens won the Israel Defense Prize.