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."

With 100 hours of video added to the site every minutes it can be hard to get noticed, so some people buy fake views.
There are many companies that will sell YouTube views, likes or comments for a fee.
Most videos have genuine views but the website wants to crack down on the small number that don't.

The organisers of Common People commissioned the inflatable structure for the event on Southampton Common on Saturday and Sunday.
The castle, measuring 23.8m by 20.7m by 12.8m, is taller than the Great Wall of China and can be used by 100 people.
It will also appear at the organisers' other festivals - Bestival on the Isle of Wight and Camp Bestival in Dorset.
Festival organiser Rob da Bank said: "We do love breaking a record and this is one of our funnest builds so far."
There is currently no record for the world's biggest bouncy castle.
Guinness World Records is yet to verify the record.
Common People, now in its second year, features Duran Duran, Primal Scream, Craig David and Public Enemy.
For the first time, a simultaneous event is also being held in South Parks, Oxford.
The current record for a bouncy castle was set in 1997 by Dana Caspersen and William Forsythe, the festival said.
The castle, measuring 19m by 19m by 12m, took six hours to erect at the Roundhouse in Camden, north London.
Working manuscripts of poems by Dylan Thomas are to go on public show for the first time.
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YouTube has warned it will clamp down on users who buy 'fake views' to make their videos look more popular than they really are.
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Festival-goers are being invited to have a go on what is claimed to be the world's largest bouncy castle.