Riot Games has launched a League of Legends server transfer tool, enabling players to move between the North America and EUW or EUNE servers.
"This upgrade has been a long time coming and we’re stoked that players now have more flexibility to choose where they play!" said Riot in making the announcement.
A transfer costs 2600 Riot Points.
Additionally, European players who joined the North American server prior to June 1, 2010 and weren't able to move to the European platform when it opened will receive a free one time transfer token.
You'll find further details in the Account Transfer FAQ.
Source: League of Legends Forums