Peterson was born in Salt Lake City, Utah and was raised in Phoenix, Arizona, where he became an Eagle Scout.

Beginning in 1940, Peterson attended Phoenix College, and in 1942 he joined the United States Navy.

He completed a civil engineering course of study at the University of Oklahoma and became a Seabee, working on projects in the Pacific Ocean theater of World War II.

On 6 April 1972, Peterson was appointed as first counselor to Victor L. Brown, the church's presiding bishop.

Peterson continued his responsibilities as a general authority until he was granted emeritus status in October 1993.