He was born on August 3, 1836 in Rochester, New York to Alvah Strong, printer of such early Rochester newspapers as the Anti-Masonic Enquirer, the Morning Advertiser, and the Weekly Republican before becoming the longtime proprietor of The Daily Democrat. His grandfather was a "physician of considerable eminence" from Warren, Connecticut who moved to Scipio, New York in 1799 and Rochester in 1821. Both his eldest uncle and father were deacons in the First Baptist Church of Rochester and helped found the Rochester Theological Seminary, over which he later presided. His youngest uncle became a 49er after losing both his wife and infant son. His younger brother, Henry A. Strong, was a wildly successful businessman and philanthropist who served as Eastman Kodak's first president.

He graduated from Yale College in 1857, having had a religious conversion during his time in college. He began his theological studies at Rochester Theological Seminary and completed his D.D. in Germany. In August 1861 he was ordained pastor of First Baptist Church of Haverhill, MA. After his short pastorate in Haverhill, he went on in 1865 to become the pastor of First Church, Cleveland, OH, and from there to become president of Rochester Theological Seminary, during which time he wrote his Systematic Theology.

His eldest son was the American psychologist and philosopher, Charles A. Strong. Diplomat Theodore C. Achilles was a first cousin, twice removed. A niece married George R. Carter and a second cousin, twice removed married Margaret Woodbury Strong.