Airberlin, Condor, Easyjet and TUIfly are flying this summer from Berlin to Rhodes; Airberlin, Condor and TUI were supposed to move all operations to the new airport on June 3rd but most probably will remain on their current facilities in Schönefeld (Condor) and Tegel (airberlin, Tuifly). Easyjet's route on the other hand is a new service and was planned to commence on June 23rd from the new airport meaning that it will certainly move on Easyjet's current Berlin base at Schönefeld.
Update 9/5/2012* Airberlin announced that they will continue flying from Tegel airport (link)
* Easyjet announced that they will continue flying from Schönefeld airport (link)
Berlin Brandenburg official announcement
Picture retrieved from airport's official website.