Use Migration Assistant to move your content, as explained here: http://support.apple.com/kb/HT4413. Once you confirm that all of your content has been successfully moved, open iTunes Preferences>Devices and check to Prevent iPods, iPhones...from automatically syncing. Connect you phone to iTunes, highlight it when it appears on the left sidebar under devices and right click (option click) on it and select Transfer Purchases. Finally, authorize the new computer for the Apple ID(s) you use to purchase content from the iTunes store (under Store>Authorize this computer). Now you can select your sync preferences in the tabs, when done, sync your phone and you should be good to go.