I literally just did EXACTLY that this weekend. Bought the 2TB seagate and took it out of the enclosure.
First, important.... FORMAT the usb drive as FAT32 first before doing anything. Afterwards you an do the update
Also update your PS4 to latest software 2.03 as older software/firmware has problems seeing the 2TB drives.
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To remove from the enclosure pry the case apart with force but carefully and the top part lifts off.
It's actually a Samsung drive inside.
Unscrew the 4 holder screws on the sides of the drive, and gently take off the silver sticky part protecting the usb/sata interface.
Take off the PS4 cover, unscrew the one big screw and slide the drive out from the side, unscrew the drive from its bracket and swap it out.
Screw in the 2Tb Samsung. Slide it back into PS3 and screw it back together and slide on the cover.
Connect the power and Turn in your ps4 in safe mode by holding down power button for 7 seconds then let go.
You will get a safe mode menu. Connect your controller via usb cable to ps4 (press ps home button) and go down to the option (re-initialise new installation) it's the last option.
Now insert a USB thumb stick with the 2.03 re-install software downloaded onto it. It's 752mb. This was the most awkward for me as I didn't multiple times and it would not read it from my UsB no matter what (just gave me an error).
You must download EU version or US version but finding EU version for me was a nightmare. Eventually found it from a link on the support forum someone shared.
Basically assuming you have the correct update in your memory stick in the PS4 folder - UPDATE folder. Your PS4 will basically now format and reinstall system software.
After few minutes it will restart your ps4 once or twice, then your back at first initial setup of PS4. Connect your wifi, log into your account etc.
Then your sorted, just have to re-download any PSN stuff and all your game updates which was a lot for me.
- Then reassemble the 500gb drive - hook it up to your computer and reformat ....
Sorted