The Collaborative International Dictionary of English v.0.48:

Transmigration \Trans`mi*gra"tion\, n. [F. transmigration, L.
   transmigratio.]
   1. The act of passing from one country to another; migration.
      [1913 Webster]

   2. The passing of the soul at death into another mortal body;
      metempsychosis.
      [1913 Webster]

WordNet (r) 3.0 (2006):

transmigration
    n 1: the passing of a soul into another body after death

Moby Thesaurus II by Grady Ward, 1.0:

89 Moby Thesaurus words for "transmigration":
   avatar, catabolism, catalysis, communication, conduction,
   consubstantiation, contagion, convection, corporealization,
   delivery, deportation, diapedesis, diffusion, displacement,
   dissemination, embodiment, emigration, expatriation, export,
   exportation, expulsion, extradition, flight, heterotopia,
   immigration, import, importation, in-migration, incarnation,
   incorporation, interchange, intermigration, materialization,
   metabolism, metagenesis, metamorphism, metamorphosis, metastasis,
   metathesis, metempsychosis, migration, mutant, mutated form,
   mutation, mutual transfer, osmosis, out-migration, passage,
   passing over, perfusion, permutation, personification,
   reembodiment, reincarnation, remigration, run, sport, spread,
   spreading, substantiation, swarm, swarming, transanimation,
   transduction, transfer, transfer of property, transference,
   transfiguration, transfigurement, transformation, transformism,
   transfusion, transit, transition, translation, translocation,
   transmigration of souls, transmission, transmittal, transmittance,
   transmogrification, transmutation, transplacement, transplantation,
   transposal, transposition, transubstantiation, travel, trek