Smith was born in Chicago on June 8, 1894. His father, Thomas Smith, was a successful fruit trader. His mother, Sadie Sanborn Smith, read a lot and had a large library. Her father was a follower of the famous evangelist R. A. Torrey. She taught her son to read when he was five. He developed a love of books that remained with him throughout his whole life. He owned more than 25,000 books.
After High School, he went to the Moody Bible Institute, where he studied from 1913 to 1914. There he became familiar with Torrey, Sunday, Ironside, Trotter, Gipsy Smith and others. His father was Trustee of the Moody Bible Institute from 1907 to 1950. From 1914 to 1917, Wilbur studied at Wooster College, where he received his BA. His received his Doctor of Divinity from Dallas Theological Seminary (which was then called the Evangelical Theological College) in 1932. At the end of his first year at Wooster College, he married Mary Irene Ostrowsky, a student at the Moody Bible Institute.
He worked as a Presbyterian minister in Ocean City, Baltimore (1922-1927), Covington (1927-30) and Coatesville (1930–37).
Charles Fuller asked Wilbur to assist in the establishment of Fuller Theological Seminary. Wilbur with other Evangelical Bible scholars such as Harold Ockenga joined the effort. From 1947 to 1963 he delivered lectures on theology and Biblical Studies. He also guided Future Pastors and performed administrative tasks (1947-1963). Between 1963 and 1971 he taught an 'English Bible' course at Trinity Evangelical Divinity School.
In 1963, Wilbur Smith resigned over a dispute over the doctrine of the infallibility of the Bible. He then became a professor at Trinity Evangelical Divinity School, Deerfield, where he taught from 1963 to 1967. From 1967 until his retirement in 1971.
In 1971 he received an honorary doctorate (Litt.D.) from Trinity Evangelical Divinity School, where was a professor in Biblical Studies.