From 1961 to 1963, Jensen served as an LDS Church missionary in the Spanish-American Mission, concentrating on teaching the gospel to Spanish-speakers in the southwestern United States.

On the November 1, 1963, Jensen married Lona Lee Child in the Manti Temple and they are the parents of six children.

He was the director of scripture coordination for the church's Curriculum Department at the time of his call as a general authority.

He previously worked for the Church Educational System as a seminary teacher and director of curriculum.

In 2004, Jensen and Lynn A. Mickelsen, also of the Seventy, were appointed to supervise the formation and publication of a Spanish-language LDS edition of the Bible.