c. 1400, handsom "easy to handle, ready at hand," from hand (n.) + -some (1). Sense extended to "fit, appropriate" (1550s, implied in handsomely), then "having fine form, good-looking, agreeable to the eye" (1580s). Meaning "generous, on a liberal scale" (of rewards, etc.) first recorded 1680s.
[Americans] use the word "handsome" much more extensively than we do: saying that Webster made a handsome speech in the Senate: that a lady talks handsomely, (eloquently:) that a book sells handsomely. A gentleman asked me on the Catskill Mountain, whether I thought the sun handsomer there than at New York. [Harriet Martineau, "Society in America," 1837]
Related: Handsomeness. For sense development, compare pretty (adj.). Similar formation in Dutch handzaam "tractable, serviceable."
Handsome is founded upon the notion of proportion, symmetry, as the result of cultivation or work; a handsome figure is strictly one that has been developed by attention to physical laws into the right proportions. It is less spiritual than beautiful; a handsome face is not necessarily a beautiful face. [Century Dictionary, 1895]