After graduating from BYU, Cannon became a vice president of Beneficial Life Insurance Company in Salt Lake City.

He was active in the Boy Scouts of America and served in the organization's Great Salt Lake Council.

Prior to his call as a general authority, Cannon served in the church as a bishop, stake president, patriarch, temple sealer, and regional representative.

From 1969 to 1972, Cannon was an assistant and counselor to W. Jay Eldredge, the general superintendent of the Young Men's Mutual Improvement Association.

In 1989, he was transferred to the newly created Second Quorum of the Seventy, where he served until being released as a general authority in 1991.