The Collaborative International Dictionary of English v.0.48:

Establish \Es*tab"lish\, v. t. [imp. & p. p. Established; p.
   pr. & vb. n. Establishing.] [OE. establissen, OF. establir,
   F. ['e]tablir, fr. L. stabilire, fr. stabilis firm, steady,
   stable. See Stable, a., -ish, and cf. Stablish.]
   1. To make stable or firm; to fix immovably or firmly; to set
      (a thing) in a place and make it stable there; to settle;
      to confirm.
      [1913 Webster]

            So were the churches established in the faith.
                                                  --Acts xvi. 5.
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            The best established tempers can scarcely forbear
            being borne down.                     --Burke.
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            Confidence which must precede union could be
            established only by consummate prudence and
            self-control.                         --Bancroft.
      [1913 Webster]

   2. To appoint or constitute for permanence, as officers,
      laws, regulations, etc.; to enact; to ordain.
      [1913 Webster]

            By the consent of all, we were established
            The people's magistrates.             --Shak.
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            Now, O king, establish the decree, and sign the
            writing, that it be not changed.      --Dan. vi. 8.
      [1913 Webster]

   3. To originate and secure the permanent existence of; to
      found; to institute; to create and regulate; -- said of a
      colony, a state, or other institutions.
      [1913 Webster]

            He hath established it [the earth], he created it
            not in vain, he formed it to be inhabited. --Is.
                                                  xlv. 18.
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            Woe to him that buildeth a town with blood, and
            establisheth a city by iniquity!      --Hab. ii. 12.
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   4. To secure public recognition in favor of; to prove and
      cause to be accepted as true; as, to establish a fact,
      usage, principle, opinion, doctrine, etc.
      [1913 Webster]

            At the mouth of two witnesses, or at the mouth of
            three witnesses, shall the matter be established.
                                                  --Deut. xix.
                                                  15.
      [1913 Webster]

   5. To set up in business; to place advantageously in a fixed
      condition; -- used reflexively; as, he established himself
      in a place; the enemy established themselves in the
      citadel.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

established \established\ adj.
   1. brought about or set up or accepted; especially long and
      widely accepted; as, distrust of established authority; a
      team established as a member of a major league; enjoyed
      his prestige as an established writer; an established
      precedent; the established Church. Contrasted with
      unestablished. [Narrower terms: entrenched;
      implanted, planted, rooted; official; recognized]
      [WordNet 1.5]

   2. securely established; as, an established reputation.

   Syn: firm.
        [WordNet 1.5]

   3. settled securely and unconditionally.

   Syn: accomplished, effected.
        [WordNet 1.5]

   4. conforming with accepted standards.
      [WordNet 1.5]

   5. shown to be valid beyond a reasonable doubt; as, the
      established facts in the case.

   Syn: proved.
        [WordNet 1.5 +PJC]

   6. (Bot.) introduced from another region and persisting
      without cultivation; -- of plants.

   Syn: naturalized.
        [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

established
    adj 1: brought about or set up or accepted; especially long
           established; "the established social order"; "distrust
           the constituted authority"; "a team established as a
           member of a major league"; "enjoyed his prestige as an
           established writer"; "an established precedent"; "the
           established Church" [syn: established, constituted]
           [ant: unestablished]
    2: settled securely and unconditionally; "that smoking causes
       health problems is an accomplished fact" [syn:
       accomplished, effected, established]
    3: conforming with accepted standards; "a conventional view of
       the world" [syn: conventional, established]
    4: shown to be valid beyond a reasonable doubt; "the established
       facts in the case"
    5: introduced from another region and persisting without
       cultivation [syn: established, naturalized]

Moby Thesaurus II by Grady Ward, 1.0:

168 Moby Thesaurus words for "established":
   accepted, acknowledged, actual, admitted, ascertained, assigned,
   assured, attested, authenticated, borne out, categorically true,
   certain, certified, chronic, circumstantiated, confirmed,
   conformable, consuetudinary, conventional, corroborated, current,
   customary, decided, deep-dyed, deep-engraven, deep-fixed,
   deep-grounded, deep-laid, deep-rooted, deep-seated, deep-set,
   deep-settled, demonstrated, deployed, determinate, determined,
   documentary, dyed-in-the-wool, effectual, embedded, embosomed,
   embossed, emplaced, engrafted, engraved, ensconced, entrenched,
   etched, everyday, factual, familiar, fast, firmly established,
   fixed, folk, generally accepted, graven, guaranteed, hallowed,
   handed down, heroic, historical, hoary, immemorial, implanted,
   impressed, imprinted, in the bag, incorrigible, inculcated,
   indelibly impressed, infixed, ingrained, ingrown, installed,
   instilled, inveterate, inwrought, irreversible, legendary, located,
   long-established, long-standing, made sure, mythological,
   nailed down, normal, not in error, objectively true, obtaining,
   of long standing, of the folk, old-line, on a rock, on bedrock,
   on ice, open-and-shut, oral, ordinary, placed, planted, popular,
   positioned, posted, prescribed, prescriptive, prevalent, proved,
   proven, real, received, recognized, regular, regulation, rooted,
   seated, secure, set, settled, settled in habit, shown, situate,
   situated, spotted, stabilized, standard, stated, stationed, stock,
   substantiated, sure-enough, tested, thorough, time-honored,
   traditional, tried, tried and true, true, true as gospel,
   true-blue, truthful, unconfuted, undenied, understood, undoubted,
   unerroneous, unfallacious, unfalse, unmistaken, unquestionable,
   unrefuted, unwritten, usual, validated, venerable, veracious,
   verified, veritable, vested, warranted, well-established,
   well-founded, well-grounded, well-set, well-settled, widespread,
   wonted, worshipful