When trying to answer this question, we run into a few snags.
First of all, who are "the Jews"? Are they children of Jewish women who are children of Jewish women? Are they part of "Jewish culture"? Are they followers of Judaism? If it wasn't confusing enough that the term applies to an ethno-religious group as well as simply religious groups, some people also have the anachronistic tendency to apply post-18th century notions of 'nations' on ancient times.
Secondly and mainly, this never happened. What did happen, is that because of its (perhaps unfortunate) geographical location, the Levant changed hands many times over the centuries. And the conquerers exerted cultural and religious influence over the inhabitants.
One of the most influentual of these were Alexander and his generals. They were such a lasting influence on the Levant, Egypt, et cetera that we have a word for this: Hellenisation (Hellas = Greece). The people who lived in the Roman province of Judea were mostly Hellenised Jews - and by this we mean the ethno-religious group that identified mainly with Jewish culture.
Under the Romans, as before, Jewish culture changed, as it had before. Even before the destruction of the temple after the first failed rebellion, Jewish religious had started decentralisating. Being part of larger empires meant being able to move more easily. And the further you get from Jerusalem, the harder it becomes to be part of a cult that centers around its temple.
Many Jews had already moved of their own volition, and after the Bar Kokhba revolt a number of rebels were shipped off as slaves. The Jewish faith was now more and more aimed at rabbinic authority rather than temple worship. And while Jews were barred from Jerusalem for 364(,25) days a year, they were still the majority in "Syria Palestina (I, II and II)" for centuries to come - perhaps until the 7th century.
To answer your actual question, like pretty much all other Mediterranean people, they had spread throughout the Mediterranean and by the first century CE there were also Jews spread across the Arabian peninsula and as far east as Iran (Persia).