Wickman was born in Seattle, Washington. He was raised in Seattle and Glendale, California. From 1961 to 1963, Wickman was a LDS Church missionary in the church's Central British Mission. After his mission, he married Patricia Farr in the Los Angeles California Temple.
Wickman graduated from the University of California at Berkley in 1964 with a bachelor's degree in political science. In 1966, Wickman was sent to fight in Vietnam as a platoon leader in the United States Army. During the war he was awarded the Bronze Star.
After his return from Vietnam, Wickman graduated from Stanford Law School in 1972. He practiced law in Glendale, California, San Diego, and San Francisco. Wickman has been awarded the Silver Beaver Award by the Boy Scouts of America.
Prior to his call as a general authority, Wickman was a bishop, stake president, and regional representative of the Twelve in the LDS Church. He became a member of the Second Quorum of the Seventy in 1994. In 2000, Wickman was transferred to the First Quorum of the Seventy.
On June 24, 2008 Wickman issued a plea to the media to make clear the distinction between the LDS Church and the Fundamentalist Church of Jesus Christ of Latter Day Saints.