The result? For the first time, more than 1,300 manuscripts are available to view on line, in a move which opens them up to a new audience of academics, students of scripture, and members of the public with an interest in Jewish history.
Via the click of a button, never-before-seen illustrated service books, Torah scrolls, scientific and astronomical treatises, and broad studies of theology and philosophy are available.
All penned in Hebrew text, they encompass works composed in Judeo-Arabic, Judeo-Greek, Judeo-Persian, Judeo-Italian, Yiddish and Ladino.
"We started by selecting works from our core collections," explained Ilana Tahan, lead curator of Hebrew and Christian Orient studies at the British Library.
"These were acquired by the British Museum over a period of 250 years, before we took them in 1977."
The process has been lengthy, having started in 2013, thanks to sponsorship from The Polonsky Foundation.
According to Ms Tahan, it has taken a great deal of time and care to upload the texts in their entirety - including digitising images from front to back, spines, maps and any additional matter. The final result are full reproductions, viewable from cover to cover.
"This has been done to enable global access," Ms Tahan said. "Previously, if you wanted to consult a manuscript, you had to come to the British Library. And even then, it was only really open to scholars and academics.
"But now, you can be living in Australia and have access to this digital surrogate."
She added: "It has opened up new avenues in terms of research. Modern technology is affording us the opportunity to see these manuscripts in a new light.
"You can now zoom into certain elements, giving you a clearer view of the way the scribe wrote the text. Until now, certain peculiarities were too small to be seen."
The notion of these texts being "stuck in the past" - written, as they were, in an ancient language and dealing with classical themes - is something Ms Tahan vehemently rejects.
Instead, she argued, they are the perfect subjects for translation into modern media.
"The Bible and the Talmud are not old texts, they are everlasting texts," she said. "They are still read every day. The Torah scroll is still a magnificent object, which is used several times every week in synagogue."
The next phase of the project, to digitise the remaining collection, is already underway.
This is mainly made up of an extensive anthology put together by Rabbi Dr Moses Gaster, who led the Spanish and Portuguese congregation in the early 19th century. The library aims to complete the task by 2019.
Ms Tahan said the project had been praised by people "of all walks of life - students, academics, members of the public, synagogues, non-Jewish organisations, pastors and librarians".
A welcome surprise, she revealed, is the interest it has sparked in visits to see the original pieces.
"Since the digitisation, there has been a surge of enquiries from people wanting to come and see the objects," she said. "However good the images are, it is not like physically handling them."
Among the thousands of uploads, Ms Tahan highlighted a Masoretic text from the 10th century and a 16th-century Pentateuch scroll measuring 52 metres in length as some of her favourites.
"Even if you have the same text copied by the same scribe, there will be differences between versions as each one is handwritten," she pointed out.
"What this project has done is raise awareness of what treasures we have here - ones which were previously limited to a very small number of viewers."
