The Collaborative International Dictionary of English v.0.48:

Triumphant \Tri*um"phant\, a. [L. triumphans, p. pr. of
   triumphare: cf. F. triomphant. See Triumph, v. i.]
   [1913 Webster]
   1. Rejoicing for victory; triumphing; exultant.
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            Successful beyond hope to lead ye forth
            Triumphant out of this infernal pit.  --Milton.
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   2. Celebrating victory; expressive of joy for success; as, a
      triumphant song or ode.
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   3. Graced with conquest; victorious.
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            Athena, war's triumphant maid.        --Pope.
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            So shall it be in the church triumphant. --Perkins.
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   4. Of or pertaining to triumph; triumphal. [Obs.]
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            Captives bound to a triumphant car.   --Shak.
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   Church triumphant, the church in heaven, enjoying a state
      of triumph, her warfare with evil being over; --
      distinguished from church militant. See under
      Militant.
      [1913 Webster]

WordNet (r) 3.0 (2006):

triumphant
    adj 1: joyful and proud especially because of triumph or
           success; "rejoicing crowds filled the streets on VJ Day";
           "a triumphal success"; "a triumphant shout" [syn:
           exultant, exulting, jubilant, prideful,
           rejoicing, triumphal, triumphant]
    2: experiencing triumph [syn: triumphant, victorious]

Moby Thesaurus II by Grady Ward, 1.0:

37 Moby Thesaurus words for "triumphant":
   ascendant, assured of success, cock-a-hoop, coming, conquering,
   crowing, crowned with success, defeating, dominant, elate, elated,
   exultant, exulting, flushed, flushed with success, fortunate,
   gloating, in ascendancy, in high feather, in the ascendant,
   jubilant, made, on the up-and-up, on top, out in front, overcoming,
   prevailing, prosperous, rejoicing, succeeding, successful,
   surefire, triumphal, undefeated, vanquishing, victorious,
   winning