Can't you search on google with site:leagueoflegends.com before you post? you'll see there are 1000 threads about this...
It's NOT Possible to "TRANSFER"/ "MIGRATE" accounts, but is possible to "SWITCH" servers, you can play on both servers with one client (the one that you have) (you have to own one account on each server)...
WWW.SilviuVlad**** launched a new version of League Of Legends Server Switcher (lolSS), version 3.0.
Merry Christmas Everyone! www.silviuvlad**** launched a new version of League Of Legends Server Switcher (lolSS), version 3.0.
To Download the latest version, and keep up to date, go to http://www.silviuvlad**** .
If you want to comment about the lolSS, go to http://www.leagueoflegends.com/board...d.php?t=268884 or SilviuVlad**** -> Contact.
[(Server Switcher = play on both servers, on European and on North American with one client, play on EU server, with uncensured graphics, and keeps the servers online, no "server busy", and more)]
Hope it helps you!
Please report bugs on http://silviuvlad.webs.com/apps/guestbook/