TLDR: No known author - it seems to have spontaneously generated from colleges.
Found on Wikipedia with no song history. The pictured version is from Beth's Music Notes.
Beth cites Albert Ernest Weir's 1918 publication The Book of a Thousand Songs. It does not have a credited composer.
I found it in the American College Song Book: A Collection of Songs from 50 Representative American Colleges, published in 1882. It was not credited to an institution, instead being included in the "Miscellaneous" part of the collection.
The identical sheet music was also published in The Northwestern Song Book: A Collection of College and Other Music... in 1879.
Another version, with a few publishing errors, can be found in the Carmina Yalensia, a Collection of Yale College Tunes published in 1867 and the Carmina Collegensia in 1868.
Another version arranged by G. W. Bemis in College Songs and Popular Ballads for Guitar, 1888
In this 1873 publication of college songs, Carmina Princetonia: A Collection of the Songs of Princeton College, they give credit to "by permission of Taintor Bros." Taintor Brothers was a publishing company.