Talbot created the first book illustrated with photography, The Pencil of Nature, published in instalments between 1844 and 1846.
The Bodleian spent two years raising the Â£2.1m needed to buy the private collection.
A library spokesman said it was a "fascinating and important resource".
The archive, which includes some of the first photographs of Oxford as well as diaries and letters, will be available to students, scholars and photographers.
But in 2017 the library plans to open a Talbot exhibition to the public.
A Bodleian spokesperson said Talbot was "most famous today for being the British founder of photography", though he was also an eminent mathematician, astronomer and archaeologist,
The polymath pioneered the use of light-sensitive paper on which to develop prints and discovered the negative of an image which could be used to produce multiple prints.
The archive includes an image made by Talbot's wife, Constance, in 1839, which may be the earliest image made by a woman.
It also includes musical scores, scientific instruments and family diaries as well as a collection of photographs by Talbot and those sent to him by other photographers.
The collection has been further enhanced after a descendent of Talbot's cousin donated 42 early photographs to the library.
Sir John Venables-Llewelyn, the great-great grandson of photographer John Dillwyn Llewelyn, was prompted to place the previously unknown photographs with the Bodleian after hearing of the appeal.
The Bodleian received Â£1.2m from the National Heritage Memorial Fund and a Â£200,000 grant from the Art Fund to help with its fund raising.
Its campaign was supported by the artist David Hockney as well as photographers Hiroshi Sugimoto and Martin Parr.
The archive of Britain's "founder of photography" William Henry Fox Talbot has been acquired by the Bodleian Library in Oxford.