Born in New Bedford, MA, Eliot arrived in St. Louis to find there was no sewer system, and sickness and disease were rampant. He spent much of his time as a minister tending to the sick, especially during typhoid and cholera epidemics. With the onset of the Civil War he organized the Western Sanitary Commission which monitored the medical services of the Northern army and its fleet during the Civil War.

He spent thirty-six years as pastor of the Unitarian Church of the Messiah, which he founded. A year after he retired, he became chancellor of Washington University, which he had helped found and funded. He refused to allow his name to be used for the University because his religious beliefs were that one was to show himself in good works, not in name recognition. He also helped found Mary Institute for girls, Smith Academy for boys, the Manual Training School, and the Academy of Science. As an author, he wrote The Discipline of Sorrow and The Life of Archer Alexander, the story of the slave he bought and then freed.

He is buried at Bellefontaine Cemetery.