Yes, but please notice that there are some requirements:
[PS4]
To save games and apps from the PS4, the requirements are as follows.
1. PS4 firmware version 4.5 (or later).
2.The external storage drive must come with a USB3.0 connector, with least 256GB of usable capacity.
Note: In general, the usable capacity would be slightly lower than advertised capacity.
3. We recommend pre-formatting the external HDD/SSD to exFAT before you use it with the PS4. If the file type is NTFS, there's a chance that the PS4 might fail to recognize the drive.
4. Once you format your external HDD, you won’t be able to use it on a PC as the PC would not recognize it.
[Xbox]
You can use external storage with the Xbox for Games & Apps, or as a Media Drive.
For Games & Apps
If you are going to play & save games on the drive, you need to format the drive on the Xbox. Also be aware of the following requirements/limitations.
1. The external storage drive must come with a USB3.0 connector, with at least 256GB of usable capacity.
Note: In general, the usable capacity would be slightly lower than the capacity specified.
2. The external storage drive should have a pre-formatted partition.
3. Once you format the drive with Xbox, it won’t be recognized by the PC without being re-formatted to its original state.
For Media Drive
Movies, music, and pictures can be saved in the drive and played with Xbox. You do not need to format the drive on Xbox for use with games and apps, and it can be recognized by the computer.