In 1989, Jensen became a member of the First Quorum of the Seventy at the age of 46. In 1993, he was made assistant executive director of the church's Priesthood Department, later becoming executive director until 2001. From 1993 to 1995, while a general authority, Jensen served as president of the church's New York Rochester Mission. In 1995, Jensen became a member of the church's Public Affairs Committee. From 1996 to 1998 he was executive director of the Church Historical Department. He served in the First Quorum of the Seventy until 1998, when he became a member of the Presidency of the Seventy, and in 2000 he also became the general president of the church's Sunday School. Jensen served in these positions until 2001. In 2004, he replaced D. Todd Christofferson as executive director of the Family and Church History Department, a position he held previously when it was just the Historical Department. In 2005, he became the first Church Historian and Recorder to serve since 1997. He served in this capacity until 2012 and was designated an emeritus general authority in October 2012.