1. Check your system software is version 4.0 or higher
First, make sure both your existing PS4 and your PS4 Pro have been updated to the latest system software. This should have happened on your existing PS4 automatically, last time you went online – but if you’re not sure, go to “Settings” and scroll down to “System Software Update”.
2. Connect to your broadband network and sign in to PSN
You’ll need to switch on both PS4 consoles and ensure they both connect to your home broadband network – either via Wi-Fi or with LAN cables – so you can sign in to PlayStation Network.
For the data transfer, only your new PS4 Pro will need to be connected to your TV. Sign in to the new console with your PSN ID and password to get started.
3. Prepare your data
Once that’s done, your PS4 Pro will detect that you’re signing in to a new console with your PSN ID and you’ll see a screen asking if you want to start transferring data from your old console to your shiny new one.
Follow the on-screen prompt to confirm you want to start the transfer process, then press and hold the Power button on your old console (until you hear a beep) to prepare your data.
4. Connect both consoles with a LAN cable
Next, connect the two PS4s together with a LAN cable, into their respective LAN ports on the back of the console.
Alternatively, you can connect each PS4 to your router, using two LAN cables. The transfer process will be exactly the same.
5. Choose the data you want to transfer
You’ll have a choice of what data you want to transfer; you can pick which applications or games are moved across (or just copy all of them), as well as your game save data, screenshots and videos you’ve captured, themes and settings.
Once you’ve chosen what data is going to be moved across, you’ll be shown how much free space will be left on the new console’s hard drive once the process is complete, and an estimate of how long the transfer will take.
6. Activate your primary PS4
Finally, you’ll be asked if you want to activate your new console as your primary PS4. This will allow you to automatically download updates, upload save game data to your PS Plus cloud storage and share content with other users.
It looks like doing all of these steps will transfer all game and save data, but will not transfer passwords or unregistered profiles or unsynched trophy data, so be sure to sync your trophies before you do the transfer!
Best Answer
As commented by Nolonar, you can copy save files to a USB storage device or, if you are a PS+ Subscriber, to the cloud.