How to sync iPhone with new mac?

Hi. I just got a new mac. I want to sync my iphone with the new computer, but how can i do that without it deleting my stuff? Can i somehow move the old backup of the iphone to the new mac? What about app data and so on?

Sync your iPhone with iTunes on your computer using USB or Wi-Fi without deleting your data.

USB syncing
Open iTunes.
Connect the iPhone to your computer using the included USB cable and select it in iTunes under Devices on the left-hand side, Click Apply, in the lower-right corner of the screen, to sync.

Wi-Fi syncing

Open iTunes
To set up Wi-Fi syncing, connect your iPhone to your computer with the included USB cable. Select your device under Devices on the left-hand side.
In the Summary tab, select "Sync with this over Wi-Fi".
Whenever the computer and the iPhone are on the same network, the iPhone will appear in iTunes, and you can sync it. The device will sync automatically when all of the following are true:

The Phone is plugged in to power
iTunes is open on the computer
The device and the computer are on the same Wi-Fi network

While the iPhone appears in the left-hand column of iTunes, you can select the content tabs and configure sync options.
Click Apply or Sync to sync the iPhone.