At the age of fourteen Johnson immigrated to Oregon Territory with his family, arriving at Marysville in 1850. On the journey along the Oregon Trail he drove a team of oxen and buried both his mother and sister on the way. At age seventeen he received his first formal education at the local public schools. Johnson then borrowed money in order to further his education and set out by ship to the Eastern Seaboard. He worked for his passage from Panama to New York City and then began at Yale University at the age of 24. In 1862 he graduated and returned to Oregon. Johnson graduated sixth out of his class of 100 at Yale. In Oregon he served as a teacher and administrator. He taught at McMinnville College (now Linfield College) from 1863–1867, eventually becoming president, and as the principal of Portland High School. After six years as principal at the high school he was then hired by the University of Oregon in 1873 as a professor of Latin. On 26 July 1876, the University of Oregon Board of Regents met (immediately upon the state land board's official acceptance of Deady Hall) and elected Johnson president. Thomas Condon, Mary Spiller, and Mark Bailey were also elected to the faculty.
During his tenure at the University, he taught Greek and Latin, and served not only as president, but as registrar, business officer, provost, dean of students, and secretary. His seventeen years as president saw great expansion of the University, including the construction of Villard Hall in 1886, and the dormitory (now Friendly Hall) in 1893. Throughout his tenure, he was a statewide advocate of the University, attempting to overcome Oregonians' objection to higher education.