The Shadow Man, and a Christmas poem called Noel, were found at Our Lady's School, Abingdon.
It is thought Tolkien got to know the school while he was a professor of Anglo-Saxon at Oxford University.
The poems were printed a year before Tolkien's first literary sensation The Hobbit was published.
The Shadow Man is an earlier version of a poem eventually published in 1962 in Tolkien's Adventures of Tom Bombadil collection.
The existence of the poems came to light after American Tolkien scholar Wayne G. Hammond got in touch with the school.
He knew from notes made by Tolkien that two of his poems appeared in a magazine he called The Abingdon Chronicle.
This was actually the 1936 annual of Our Lady's School, which was then run by the Sisters of Mercy.
School principal Stephen Oliver said: "At first we couldn't find the 1936 edition and referred Mr Hammond to the archives of the Sisters of Mercy in London.
"Then, while preparing for an event for former pupils of the school, we uncovered our own copy and I saw the two poems Mr Hammond had been looking for. "
The school hopes to put the annual on display at a future exhibition.
Two poems by author JRR Tolkien have been discovered in a 1936 copy of a school annual.