At the time of Eldred's birth, a new Presiding Patriarch was usually chosen based on the principle of patrilineal succession. However, instead of choosing Eldred to replace his father, Church President Heber J. Grant appointed Eldred's cousin Joseph Fielding Smith to be Presiding Patriarch in 1942. After Joseph Fielding Smith was released from the position in 1946 by Church President George Albert Smith, Eldred was selected as the next Presiding Patriarch.
Smith was ordained in 1947 and served in that calling for the next 32 years. He regularly spoke in the semiannual Church General Conferences but was only rarely assigned to visit local Stakes of the Church.
During his tenure as Presiding Patriarch, Smith's primary duty was to travel to areas of the world where there were no patriarchs in order to bestow patriarchal blessings upon worthy Latter-day Saints.
In 1979 Smith was released from active duties and designated Patriarch Emeritus. The reported reason for this change was the increase of availability of Stake Patriarchs throughout the Church. As was announced by the Church in General Conference: "Because of the large increase in the number of stake patriarchs and the availability of patriarchal service throughout the world, we now designate Elder Eldred G. Smith as a Patriarch Emeritus, which means that he is honorably relieved of all duties and responsibilities pertaining to the office of Patriarch to the Church.
Today, Smith is considered to be an emeritus General Authority of the Church. He remains an ordained patriarch and is still permitted to give patriarchal blessings. However, he is no longer sustained by the Church as a "prophet, seer, and revelator" as he was from 1947 to 1979. On 9 January 2007, Smith celebrated his 100th birthday. He is only the second General Authority in the history of the Church to reach the age of 100, the first being Joseph Anderson, who died in 1992 at the age of 102.
The Church has not stated whether or not it will appoint a new Presiding Patriarch upon Smith's death.