Jews were resettled across the west and near east in multiple “disaporas” really. Most notably, the Roman one took place after ~70 CE, scattering Jews around what was then the Roman Empire – sometimes because they were prohibited from staying in what is today Palestine/Israel, and sometimes because they were explicitly sold into slavery. Before that, though, robust and learned Jewish populations existed around the Greco-Roman world – perhaps partly because of Alexander the Great.
As the Western Empire fell, various Germanic tribes pushed into the former imperial territories, some leaving large marks on the map to this day; see places like Lombardy in Italy or Saxony in Germany; or even some national names, such as France referring to the Germanic tribe known as the Franks (this is reflected in the German name for the country: Frankreich, or “Empire of the Franks”). No doubt these early migrations themselves also pushed other relatively dispossessed people, such as Jews, around.
In the Middle Ages, Jews were often not welcome to settle as farmers and were, ironically perhaps, unwanted as vassals to feudal lords. (There are some exceptions to this, of course. I believe by the time of the plague, Jews played a large part in growing wine in the Loire river valley, for instance.) This pushed them into cities, where they were usually still heavily restricted, segregated into ghettos, and unable to perform many gentile trades. Because of corny medieval usury laws, one area they were allowed to be quite successful was in money lending. And in the nascent capitalist economies of the 12th century, finance was already becoming a critical economic function.
All that just made more expulsions inevitable. Of course, the tough side of the money lending business even today is you need to be paid back, and the bread and butter of the business is lending to people with resources to make good on their debts. Unfortunately, this often meant making money loaning money to powerful princes or bourgeois merchants who could conveniently expel you on trumped up charges after you loaned out some money at a ridiculous, but perhaps necessarily high under the circumstances, interest rate.
So, all in all, how they ended up where they did is rather unsurprising. They were automatically attracted to places where they could work, and the merchant economies of northern Europe that developed in the late medieval period made for sensible places to settle (or be forced to by hostile lords elsewhere) .