Burton was hired by the LDS Church as the assistant budget officer in 1977. Burton later accepted a position as the executive secretary to the church's
presiding bishopric. In October 1992, Burton was called by
Robert D. Hales as first counselor in the presiding bishopric. In 1994, he was again called as first counselor to the new presiding bishop,
Merrill J. Bateman. On December 27, 1995, when Bateman became the president of
Brigham Young University, Burton became the church's Presiding Bishop--a post roughly equivalent to chief operating officer. Burton called
Richard C. Edgley as his first counselor and
Keith B. McMullin as his second counselor. Burton was a prominent voice from the LDS Church on the issue of Utah immigration legislation in 2011. Burton oversaw the LDS Church's $1.5 billion mixed-use development project called
City Creek Center in downtown
Salt Lake City. Burton and his counselors were released on 31 March 2012 and designated as
emeritus general authorities. ==Civic service==