Harris was born near Upper Makefield Township, Pennsylvania. He earned a B.S. from the University of Delaware (1931), a Th.B. (1935) and a Th.M. (1937) from Westminster Theological Seminary, an A.M. from University of Pennsylvania (1941), and a Ph.D. from Dropsie College (1947).
He was licensed as a minister in the Presbyterian Church in 1935, joined to the newly formed Orthodox Presbyterian Church (then called Presbyterian Church of America) in 1936, joined those forming the Bible Presbyterian Church in 1937, and was in 1956 moderator of a new off-shoot denomination, the Bible Presbyterian Synod (BPS). He was involved on the committee that brought about the merger of the BPS with another denomination to become the Reformed Presbyterian Church, Evangelical Synod (RPCES) in 1965, and then the RPCES, along with its education institutions Covenant College and Covenant Theological Seminary, became part of the Presbyterian Church in America in 1982, at which time Harris was elected moderator of the 10th General Assembly of that body.
He was part-time instructor in Hebrew at the University of Pennsylvania (1946-1947) and then taught for twenty years at Faith Theological Seminary (1937-1956). He resigned from that institution because of his belief in the propriety of denomination-controlled institutions, and he then helped found the Covenant Theological Seminary, which was a denominational institution and where he was chairman of the Old Testament department until he retired in 1981. He taught as an adjunct professor of Old Testament at Knox Theological Seminary at its founding in 1989.
Harris's first wife, Elizabeth K. Nelson, was born on April 30, 1910 and died in 1980. He was remarried to Anne P. Krauss and lived in Quarryville, Pennsylvania.
He also served as editor of The Theological Wordbook of the Old Testament and a was contributing editor to the Zondervan Pictorial Encyclopedia of the Bible. He was contributed articles to the Wycliffe Bible Commentary and the Expositor's Bible, and he served as chairman of the Committee on Bible Translation for the New International Version.