Step 1. Connect Your iPhone to new Mac with USB cable. iTunes should launch automatically.
Step 2. Click on the iPhone image and name in the left hand drawer in the program. The phone’s information should show up on the right.
Step 3. Click on the tabs in the window and choose what information you would like to sync. You can sync photos, music, contacts, applications and ringtones.
Step 4. Press “Apply” in the lower-right corner of the screen to sync the iPhone with the computer. You will be asked in your first sync whether you wish to merge data between computer and phone, replace the data on the phone, or replace data on the computer. In the case of a new Mac you will likely want to replace data on the computer, which backs up your iPhone data on your new computer.
After finishing the above steps, you have just successfully transferred all your purchased files from iPhone to your new Mac.
How to Sync iPhone to New Mac with iTunes