Old English heorte "heart (hollow muscular organ that circulates blood); breast, soul, spirit, will, desire; courage; mind, intellect," from Proto-Germanic *hertan- (source also of Old Saxon herta, Old Frisian herte, Old Norse hjarta, Dutch hart, Old High German herza, German Herz, Gothic hairto), from PIE root *kerd- "heart."
Spelling with -ea- is c. 1500, reflecting what then was a long vowel, and the spelling remained when the pronunciation shifted. Most of the modern figurative senses were present in Old English, including "memory" (from the notion of the heart as the seat of all mental faculties, now only in by heart, which is from late 14c.), "seat of inmost feelings; will; seat of emotions, especially love and affection; seat of courage." Meaning "inner part of anything" is from early 14c. In reference to the conventional heart-shape in illustration, late 15c.; heart-shaped is from 1744.
Heart attack attested from 1875; heart disease is from 1864. The card game hearts is so called from 1886. To have one's heart in the right place "mean well" is from 1774. Heart and soul "one's whole being" is from 1650s. To eat (one's own) heart "waste away with grief, resentment, etc." is from 1580s.