also clearinghouse, 1805, from clearing + house (n.). The original was established 1775 in London by the bankers for the adjustment of their mutual claims for checks and bills; later the word was extended to similar institutions.
CLEARING, is a method adopted by city bankers, for exchanging the drafts on each others houses, and settling the differences.--Thus at a stated hour in the afternoon, a clerk from each attends at the Clearing House, where he brings all the drafts on the other bankers, which have been paid into his house during the course of the day; and, having debited their different accounts with the articles which he has against them, he deposits them in their proper drawers, (a drawer being here allotted to each banker:) he then credits their accounts respectively, with the articles which they have against him, as found in his drawer. Balances are then struck on all the accounts, and the differences are transferred from one to another, until they are so wound up, that each clerk has only to settle with two or three others, which is done in cash, or Bank of England notes. [P. Kelly, "The Elements of Book-Keeping," London, 1805]