I broke my iphone 4 a few weeks ago and I've been using a Blackberry while I wait for iphone 5. My question is , when I synch the iphone 5 with my itunes, will all my contacts and apps automatically go into the new phone?

Hi. I broke the screen on my iphone 4 a few weeks back rendering the touch screen useless. I've been using an old Blackberry while I await my iphone 5. My question is, will all my contacts and apps sync with the iphone 5 automatically when I connect it to itunes for the first time? I regularly backed up my iphone 4 to icloud so i am hoping that my contacts and all other info is not lost. I can no longer unlock my iphone 4 to view my contacts because as I stated earlier, the touch screen is no longer responding. Any info would be greatly appreciated. Thanks!