The Collaborative International Dictionary of English v.0.48:

Elegant \El"e*gant\, a. [L. elegans, -antis; akin to eligere to
   pick out, choose, select: cf. F. ['e]l['e]gant. See Elect.]
   1. Very choice, and hence, pleasing to good taste;
      characterized by grace, propriety, and refinement, and the
      absence of every thing offensive; exciting admiration and
      approbation by symmetry, completeness, freedom from
      blemish, and the like; graceful; tasteful and highly
      attractive; as, elegant manners; elegant style of
      composition; an elegant speaker; an elegant structure.
      [1913 Webster]

            A more diligent cultivation of elegant literature.
                                                  --Prescott.
      [1913 Webster]

   2. Exercising a nice choice; discriminating beauty or
      sensitive to beauty; as, elegant taste.

   Syn: Tasteful; polished; graceful; refined; comely; handsome;
        richly ornamental.
        [1913 Webster]

WordNet (r) 3.0 (2006):

elegant
    adj 1: refined and tasteful in appearance or behavior or style;
           "elegant handwriting"; "an elegant dark suit"; "she was
           elegant to her fingertips"; "small churches with elegant
           white spires"; "an elegant mathematical solution--simple
           and precise and lucid" [ant: inelegant]
    2: suggesting taste, ease, and wealth [syn: elegant,
       graceful, refined]
    3: displaying effortless beauty and simplicity in movement or
       execution; "an elegant dancer"; "an elegant mathematical
       solution -- simple and precise"

Moby Thesaurus II by Grady Ward, 1.0:

228 Moby Thesaurus words for "elegant":
   Attic, Babylonian, Ciceronian, Corinthian, advantageous, aesthetic,
   aesthetically appealing, apt, arabesque, artistic, attractive,
   august, auspicious, awe-inspiring, awful, barbaric, baroque,
   beauteous, beautiful, becoming, beneficial, benevolent, bon, bonny,
   braw, bueno, busy, capital, chaste, chic, chichi, choice,
   civilized, classic, classy, clear, clever, clothes-conscious,
   cogent, comely, commendable, cosmopolitan, courtly, cultivated,
   cultured, dainty, dapper, dashing, debonair, decent, decorous,
   delicate, deluxe, dignified, direct, discerning, discriminating,
   dressed to advantage, dressed to kill, easy, elaborate,
   endowed with beauty, estimable, euphemistic, euphuistic, excellent,
   expedient, exquisite, extravagant, eye-filling, facile, fair,
   famous, fancy, fashionable, fastidious, favorable, fine, finished,
   flamboyant, florid, flowerlike, flowery, flowing, fluent,
   formalistic, frilly, fussy, genteel, glorious, good, goodly,
   goody good-good, goody-goody, graceful, gracile, gracious, grand,
   grandiose, handsome, healthy, heavy, helpful, high-wrought,
   imposing, impressive, in, ingenious, jaunty, kind, labored,
   laudable, limpid, lovely, lucid, luxuriant, luxurious, magnificent,
   majestic, mincing, modest, modish, moresque, namby-pamby, natty,
   natural, neat, nice, nifty, nobby, noble, opulent, ornate,
   ostentatious, overelaborate, overelegant, overlabored, overnice,
   overprecise, overrefined, overworked, overwrought, palatial,
   pedantic, pellucid, perspicuous, picturesque, plain, pleasant,
   pleasing, plush, polished, posh, precieuse, precious, precisian,
   precisianistic, precisionistic, pretty, pretty-pretty, princely,
   profitable, proper, proud, pulchritudinous, pure, puristic, rare,
   recherche, refined, regal, restrained, rich, ritzy, rococo, round,
   royal, seemly, select, sharp, simpering, simple, skillful, sleek,
   smart, smooth, smug, snazzy, soigne, soignee, sophisticated, sound,
   spiffy, splendacious, splendid, splendiferous, spruce, stately,
   straightforward, style-conscious, stylish, suave, subtle,
   sumptuous, superb, superfancy, superfine, superior, swank, swanky,
   swell, tasteful, terse, tricksy, trig, trim, tripping, unaffected,
   unlabored, urbane, useful, valid, very good, virtuous, well-bred,
   well-dressed, well-groomed, with it



The Jargon File (version 4.4.7, 29 Dec 2003):

elegant
 adj.

    [common; from mathematical usage] Combining simplicity, power, and a
    certain ineffable grace of design. Higher praise than ?clever?, ?winning?,
    or even cuspy.

    The French aviator, adventurer, and author Antoine de Saint-Exup?ry,
    probably best known for his classic children's book The Little Prince, was
    also an aircraft designer. He gave us perhaps the best definition of
    engineering elegance when he said ?A designer knows he has achieved
    perfection not when there is nothing left to add, but when there is nothing
    left to take away.?


The Free On-line Dictionary of Computing (30 December 2018):

elegant

   (From Mathematics) Combining simplicity, power, and a certain
   ineffable grace of design.  Higher praise than "clever",
   "winning" or even cuspy.

   The French aviator, adventurer, and author Antoine de
   Saint-Exup'ery, probably best known for his classic children's
   book "The Little Prince", was also an aircraft designer.  He
   gave us perhaps the best definition of engineering elegance
   when he said "A designer knows he has achieved perfection not
   when there is nothing left to add, but when there is nothing
   left to take away."

   [Jargon File]

   (1994-11-29)