Henry Kemble Oliver was born in Beverly, Massachusetts, on November 24, 1800, the son of the Reverend Daniel Oliver and Elizabeth Kemble of Boston. He was named Thomas Henry Oliver but changed this to Henry Kemble Oliver in 1820 to preserve his mother's name. His ancestor was Thomas Oliver of Bristol, England, who emigrated to American in 1632 and settled in Boston. Henry Kemble Oliver was educated at Boston Latin School, Phillips Academy Andover, Harvard University, and Dartmouth College, from which he graduated in 1818. In 1862, Harvard granted him the degrees of A.B. and A.M. (Genealogical note: Dr. Oliver Wendell Holmes's grandfather and Henry Kemble Oliver's grandmother were brother and sister.)

Oliver was married on August 20, 1825, to Sarah Cook, daughter of Captain Samuel Cook and Sarah Chever of Salem. They had two sons and five daughters: Henry K., Jr., Samuel C., Maria, Sarah, Emily, Mary, and Ellen.

Oliver taught in Salem schools for twenty-five years. His military career began in 1821 when he joined the Salem Light Infantry. Twelve years later, he was Lieutenant-Colonel of the 6th Massachusetts Infantry and was soon promoted to its colonelcy. In 1844, he accepted the office of Adjutant General of the state troops. In the Ancient and Honorable Artillery of Boston, he gained a captaincy by 1846. During the Mexican War, he raised the only volunteer regiment to go to Mexico from New England, known as the 1st Massachusetts Volunteers.

Other positions of authority held by Oliver were: mayor of Lawrence, Massachusetts, in 1859; state treasurer during the Civil War; chief of the Labor Bureau; Labor Reform candidate for governor; State Board of Education member; and mayor of Salem, 1877-1880.

He sang for a Boston church as a boy, and, at the age of twenty-three, began his thirty-two-year career as an organist at churches in Salem and Lawrence. He organized the Salem Mozart Association, serving as its president, organist, and director. He wrote church music, his best known tune being "Federal Street," which he was called upon to conduct at the Peace Jubilee in Boston on June 25, 1872. He was an excellent performer on the organ, violoncello, flute, and pianoforte.

In 1873, Oliver retired to spend the later years of his life in Salem. He died on August 12, 1885, as the consequence of paralysis of the brain. His funeral was conducted from the North Street Unitarian Church of Salem, of which he was a member. He was buried in the Broad Street Cemetery. The monument on his grave is a natural boulder with a representation of organ pipes sculpted in relief.