Another fine example of the speech of the wild frontier of the US of A, this came to life sometime in the 1830s to express the idea of confusing or disconcerting another person.
Whose invention it was we have no idea, except that he shared the bombastic, super-confident attitude towards language that also bequeathed us (among others) absquatulate, bloviate, hornswoggle and sockdolager.
It has much about it of the itinerant peddler, whose qualifications were principally a persuasive manner, the self-assurance of a man who has seen every sort of reluctant customer and charmed them all, and a vocabulary he had enlarged by gross disfigurement of innocent elements of the English language. In this case, the original seems to have been discompose or discomfit. In the early days, it sometimes appeared as discombobracate or discomboberate.
Here’s an example of a snake-oil salesman at work in 1860 (except that he was praising the water from the Louisville artesian well rather than any manufactured remedy). It was said to have been taken down verbatim: “It discomboberates inflammatory rheumatism, sore eyes, scrofula, dyspepsia, and leaves you harmonious without any defalcation, as harmonious systematically as a young dove”.
Worth a dollar a drop ...