The official Pokémon Global Link website has announced the details for the Eevee Evolution distribution. The Pokémon will be available starting May 19th, 2011. The new update is posted below.

Press Release

Befriend Eevee's Evolution on May 19th! If you visited the Pokémon Fun Zone on Pokemon.com and played the game to earn one of Eevee's evolutions, you can befriend the Pokémon starting on May 19th. Sign into the Pokémon Global Link using your Pokémon Trainer Club account information, then visit the promotions page to befriend the Pokémon. Then, you can transfer that Pokémon into your copy of Pokémon Black Version or Pokémon White Version when you wake your Pokémon in the Pokémon Dream World!

Source: http://en.pokemon-gl.com/information/?infoto=121