Old English hælþ "wholeness, a being whole, sound or well," from Proto-Germanic *hailitho, from PIE *kailo- "whole, uninjured, of good omen" (source also of Old English hal "hale, whole;" Old Norse heill "healthy;" Old English halig, Old Norse helge "holy, sacred;" Old English hælan "to heal"). With Proto-Germanic abstract noun suffix *-itho (see -th (2)).
Of physical health in Middle English, but also "prosperity, happiness, welfare; preservation, safety." An abstract noun to whole, not to heal. Meaning "a salutation" (in a toast, etc.) wishing one welfare or prosperity is from 1590s. Health food is from 1848.