In 1969, he succeeded G. Carlos Smith as the leader of the YMMIA. In November 1972, Eldredge became the first general superintendent of that organization to be called the general president of the YMMIA. Just weeks after this change in terminology, Eldredge was released and was succeeded by his second counselor, Robert L. Backman.
Prior to his service in the YMMIA, Eldredge had been a church mission president in the eastern United States and was the first president of the Parley's Stake of the church.
Eldredge was born in Salt Lake City, Utah, to Walter Joshua and Lutie S. Nicholson Eldredge. He married Marjory Ormsby Hyde, a great-granddaughter of LDS Church apostleOrson Hyde. Together they had five children. He died in Salt Lake City on his 89th birthday.