Old English blæcan, of cloth or fabric, "to make white by removing color, whiten" (by exposure to chemical agents or the sun), from Proto-Germanic *blaikjan "to make white" (source also of Old Saxon blek, Old Norse bleikr, Dutch bleek, Old High German bleih, German bleich "pale;" Old Norse bleikja, Dutch bleken, German bleichen "to make white, cause to fade"), from PIE root *bhel- (1) "to shine, flash, burn," also "shining white."
The same root probably produced black, perhaps because both black and white are colorless, or because both are associated in different ways with burning. Compare Old English scimian meaning both "to shine" and "to dim, grow dusky, grow dark," which is related to the source of shine. Intransitive sense "become white" is from 1610s. Related: Bleached; bleaching. The past participle in Middle English was sometimes blaught.
1881, "a bleaching agent;" 1882, "an act of bleaching;" probably directly from bleach (v.). The Old English noun blæce meant "leprosy;" Late Old English also had blæco "paleness," and Middle English had blech "whitening or bleaching agent," but the modern words seem to be independent late 19c. formations from the verb.