Stone was born in Chapin, Idaho. He graduated from Brigham Young High School in Provo, Utah, in 1920. He worked as a bookkeeper and business manager, eventually becoming an executive with Safeway stores. Prior to his call as a general authority, he served as a bishop, stake president, and regional representative of the Twelve Apostles. In 1972, after serving as the president of the Salt Lake Temple, Stone became an Assistant to the Quorum of the Twelve Apostles. He served in this position until 1976, when the church abolished the position of Assistant to the Twelve. At this time, Stone became a member of the First Quorum of the Seventy.
In 1980, Stone was released from active duties in the church and given general authority emeritus status. He died at his home in Salt Lake City, Utah.