Dictionary:

transmigrate

  (trăns-mī'grāt', trănz-)

1. To migrate.
2. To pass into another body after death. Used of the soul.

[Latin trānsmigrāre, trānsmigrāt- : trāns-, trans- + migrāre, to migrate; see migrate.]

verb

1. To leave one's native land and settle in another: emigrate, immigrate, migrate. See approach/retreat.
2. To change habitat seasonally: migrate. See move/halt.

Movement from one site to another, which may entail the crossing of some usually limiting membrane or barrier, as in diapedesis.

1. diapedesis.
2. change of place from one side of the body to the other.

The verb has 2 meanings:

Meaning #1: be born anew in another body after death
  Synonym: reincarnate

Meaning #2: move from one country or region to another and settle there
  Synonym: migrate