Oaks was born and raised in Provo, Utah. He studied accounting at Brigham Young University (BYU), then went to law school at the University of Chicago, where he was editor-in-chief of the "University of Chicago Law Review" and graduated in 1957 with a J.D. "cum laude". After law school, Oaks clerked for Chief Justice Earl Warren at the U.S. Supreme Court. After three years as an associate at the law firm Kirkland & Ellis, Oaks returned to the University of Chicago in 1961 as a professor of law. He taught at Chicago until 1971, when he was chosen to succeed Ernest L. Wilkinson as the president of BYU. Oaks was BYU's president from 1971 until 1980 and was then appointed to the Utah Supreme Court, on which he served until his selection to the LDS Church's Quorum of the Twelve Apostles in 1984.