Riot Games has opened paid transfers between its North American and European regional servers.
You'll have to cough up 2,600 Riot Points - about $20 - for the privilege, but European players who joined the North American server prior to June 1st 2010 and weren’t able to move to the European platform when it opened will receive a free transfer token.
You can find transfers in the Other section of the in-game store, but be warned - it's one way only. If you change your mind, you'll have to pay up again.
Transferred players will keep their name wherever possible, and will retain level, champions, skins, runes, extra rune pages, summoner icons, IP, remaining RP, hidden MMR, games played, previous referrals and any unused referral rewards.
You will lose your ranking, and will have to start again in a new league, which you'll be automatically placed in after one ranked match. You'll also lose your friends list, any Tribunal Honor Points, forum badges, or Justice Rating.