The most ancient Hebrew texts are written in a script very different—but not wholly dissimilar—from that used today, although there is a one-to-one correspondence between their letters. Aaron Koller explains how and why the transition took place, and what the Talmud has to say about it:
When Judah was conquered by the Babylonians, the Judeans found themselves in exile in a kingdom that had adopted the Aramaic alphabet. While Akkadian had been the official language of Babylonia for centuries, by the 6th century BCE, it was mostly relegated to elite [usage]. In its place, due to heavy immigration of Arameans south into Mesopotamia, Aramaic had gained dominance as the spoken language, and Assyrian and Babylonian kings employed scribes of both languages.
Judeans . . . quickly adapted to the use of Aramaic writing, enabling them to take part in the economy and society. Nevertheless, Judeans in the Babylonian exile continued to use Old Hebrew script as well, especially when writing in Hebrew.
The Persian conquest of Babylonia cemented the transition—but not completely. Koller observes that the Old Hebrew script continued to be used alongside the new even after the destruction of the Second Temple.
More about: Ancient Persia, Biblical Hebrew, Hebrew alphabet