Adonijah Strong Welch was born in East Hampton, Connecticut on April 12, 1821. At the age of eighteen, he travelled to Jonesville, Michigan with his parents. He enrolled at the University of Michigan sophomore class in 1843; in 1844 he was appointed as the first principal of the Preparatory Department, and graduated in 1846. Following college, Welch studied law in the office of Lothrop and Duffield and was admitted to the bar, although instead of practicing law he chose to return to Jonesville where he organized a Union School. In 1848, Welch left Michigan for California in hopes of finding gold; he returned due to poor health, and began campaigning for the establishment of a Normal College in the state of Michigan. In 1851 he was named the first principal of the newly founded Michigan State Normal College.

The years of Adonijah Strong Welch's administration were beset with difficulties; he was tasked with assembling a faculty, creating a curriculum, and adopting policies that would guide the MSNC future. Two years after its founding, instruction in agriculture and mechanical arts were transferred to the Michigan Agricultural College. In 1859, the MSNC building was lost to fire, and in 1861 the United States Civil War had a huge impact on both the students and faculty; Welch visited the E Company, made up largely of MSNC students, as they marched across Virginia.

While MSNC president, Welch published two books, An Analysis of the English Sentence and Treatise on Object Lessons.

Because of his poor health, Welch took a leave of absence in 1859, during which he traveled throughout Europe; in 1865 he resigned and moved to Jacksonville, Florida, where he went into business with his brother-in-law and taught in a Freedmen's school. He took an interest in politics and joined the Republican Party; Welch was elected to the United States Senate to finish an un-expired term. In 1868, Welch was elected President of the Iowa Agricultural College, later Iowa State College. He served as President until 1883, though he remained a faculty member until 1889. Welch died on March 13, 1889 in Pasadena, California, and was buried at the Iowa State College cemetery in Ames, Iowa.