I tried to look it up, but it's not that easy to find the answer. Wiki gives the classic explanation, that it was 17th/18th century English prescriptivism, with the rise of mass education, following Latin logical structures (it cannot have been from ethnic German influence, btw, because its loss is common to English-English as well).
https://en.wikipedia.org/wiki/Double_negative#English
However I've seen other sources indicating that this isn't really historically correct, and the double negative was already being excluded from English for internal functional reasons, i.e. it doesn't really play nicely with Germanic grammar, which is why none of the other West Germanic languages allow it. So it was a sort of temporary innovation in English that didn't ever take very well.
In other languages, it might work fine, because you have other ways of making the point clear potentially, but in English I really think the use of double negation tends to impede long logical sentences. To be clear, you end up needing other devices to signal that it's 'emphatic double negation' and not 'negating double negation,' and this just makes a mess of things.