The youngest of four children, Bouchet attended New Haven High School from 1866 to 1868. He continued his education at the Hopkins Grammar School, where he studied mathematics and history in addition to learning Latin and Greek. Bouchet graduated valedictorian of his class from Hopkins in 1870.

That fall, Bouchet entered Yale College (later renamed Yale University) in pursuit of a bachelor’s degree—a remarkable endeavor for the time, as there were few opportunities for African Americans seeking higher education. After graduating from Yale with his bachelor’s in 1874, Bouchet stayed on for two more years and completed his Ph.D. in physics—making him the first to earn a doctorate degree in the United States—in 1876. With this accomplishment, Bouchet joined a select group of academics; only a handful of other people had earned that same degree in the country’s history by this time.Despite his impressive achievement, Bouchet could not land a college professorship due to his race. He instead went to work at the School for Colored Youth in Philadelphia. For more than 25 years, Bouchet taught chemistry and physics at one of the few institutions that offered African Americans a rigorous academic program. But the school changed its direction in 1902 to focus on offering vocational training.