The papers, showing drafts of the poems Unluckily for a Death and Into her Lying Down Head, were bought by Swansea University at an auction in New York.
They will go on public display at the university's Bay Campus library on International Dylan Thomas Day - 14 May.
The drafts include 25 pages in Thomas's minuscule handwriting.
Thomas's granddaughter Hannah Ellis said: "It is wonderful that Swansea University are putting so much energy and effort into new ways to study and research Dylan Thomas.
"Having these manuscripts in Britain, along with the notebook they acquired in 2014, will help people to see the meticulous craft that my grandfather put into his work, and allow them to understand that he was a significant 20th Century writer."
The papers show the poet revising imagery and word choice, and working out rhythmic structures, including diagrams of his tentative rhyme scheme and small drawings where he appears to be visualising his imagery.
Jeff Towns, owner of Dylan's Bookstore, said: "These papers reveal intimate and detailed records of the poet's creative process and will be invaluable to future generations of students and academics."
The manuscripts will be kept in the university's Richard Burton Archives, which already house the Dylan Thomas notebook.
Prof John Spurr, head of the university's College of Arts and Humanities, said: "These manuscripts offer a fascinating insight into the craft of one of our greatest 20th Century poets, and it is fitting that they will be kept in Dylan's home town, and be accessible to scholars and the general public."
Working manuscripts of poems by Dylan Thomas are to go on public show for the first time.