I bought the 2TB version and it does work with the PS4 (current version 4.50). At first it said it didn't support it but after I restarted my PS4 it worked. Currently works as intended. There's 1.84TB usable after formatting. It took 19 minutes to transfer 3 games (118.3 GB) over from the internal hard drive to this external hard drive. Will update if anything arises.

Edit: It had been a little over two months and its still working as intended. To answer a common question:
It works out of the box. Literally just plug it into your ps4 go to devices under settings then USB storage devices. It should pop up under there, select it then it will say "Format as extended storage" and select that. The support for external hard drives is absolutely great. If you have a TON of downloadable games then you can simply just have multiple external hard drives and download all you games to them. Then you can just plug in the external hard drive with the game you want and you're good to go. I highly recommend looking up how to set it up if you are still having trouble. It is very easy.

I've often complained about Amazon rating system for tech products and external USB hard drives are great example of the problem. Simply, it's saturated market with lots of viable options, while impact of "picking wrong" is quite profound. You can wake up one day and find out that your data is gone. Reviews here don't help much: you read 1 star review saying "drive arrived dead", then you have 5 star review saying "drive is great". Which one to trust? Especially since I would prefer "dead on arrival" HDD to one that dies after 1 year of working.

In my case - now that Nintendo Switch is coming - I wanted to download all digitally purchased games I have for Wii U and store them along with save games on one drive. Testing tech components is a hobby of mine and I've decided to go all in - purchasing 3 external HDD drives so I can test how they work and pick the best one. The drives I've tried out are:

WD 1TB Black My Passport Portable External Hard Drive - USB 3.0 - WDBYNN0010BBK-WESN
https://www.amazon.com/Black-Passport-Portable-External-Drive/dp/B01LQQHI8I/ref=as_li_ss_tl?ie=UTF8&linkCode=ll1&tag=pers0nal-20&linkId=8ae37a7d7b9d5f8cf95b8b36f9e0e5e1

HGST Touro S 1TB 7200RPM High-Performance Portable Drive, Platinum (0S03694)
https://www.amazon.com/HGST-High-Performance-Portable-Platinum-0S03694/dp/B00IVFDQFM/ref=as_li_ss_tl?s=pc&ie=UTF8&qid=1487637450&sr=1-1&keywords=hgst+external+1tb&linkCode=ll1&tag=pers0nal-20&linkId=d813ac13cad5cfa89dd1cbc0bd5e087e

Seagate Expansion 1TB Portable External Hard Drive USB 3.0 (STEA1000400)
https://www.amazon.com/dp/B00TKFEEAS/ref=as_li_ss_tl?ie=UTF8&linkCode=ll1&tag=pers0nal-20&linkId=760fd69a7e53bfff98e624d465627daf

Now, on the Seagate drive I'm reviewing here - it's pretty solid HDD. Read/write statistics (90+MB/s) are great for the price. HGST (Hitachi) Touro beats it performance-wise but it's $30+ more expensive. What is more important are peripherals - HGST spins on 7200 rpm so it also draws more power. Which is quite important because of known problems with Wii U supplying enough power though it's USB ports. Y cable is a must for worry free operation regardless of which external drive you pick for your Wii U:

https://www.amazon.com/Micro-B-External-Seagate-Toshiba-Hitachi/dp/B005M0ICG2/ref=as_li_ss_tl?s=pc&ie=UTF8&qid=1487708286&sr=1-1&keywords=y+cable+wii+u&linkCode=ll1&tag=codeproject-20&linkId=cbd46736cfae87a00345b789f6fc5907

During normal usage I couldn't notice any difference between 3 HDDs on Wii U. Probable cause are 2.0 USB ports that are on Wii U - simply there is not enough throughput for performance differences to be visible.

The biggest issue I have with Seagate is historical fail rate. Few years ago Seagate drives had 15%+ fail rate which is catastrophic. I bought Seagate Central HDD in 2013 only to replace it a year later. That's also why I got WD and HGST to test - historically those brands have lower fail rates for their drives. HGST is way better than both Seagate and WD; but unfortunately you won't find it in stock here on Amazon as much as Seagate and WD. This is probably because WD owns HGST/Hitachi and wants to push WD as consumer brand.

In the end, my pick is WD 1TB Black My Passport. Looking at historic data, warranty info and number of 1 star reviews here on Amazon I felt more confident in storing data on that drive. Seagate HDD is solid pick and great value, but if for same amount of money you can get hard drive that has lower fail rate and better warranty - why wouldn't you buy it instead?

I avoid linking externally from Amazon because those often get edited out of review. But if you want more data - like historic fail rates, more testing info and answers to your questions, leave a comment on this review and I'll be glad to respond and help! And if this review helped you, please like it ;). Here are also answers to few questions that I see are often asked on this HDD:

* This drive will work as expansion storage for consoles. This includes Wii U, PS4, Xbox One. So will WD drive that I recommend.

* You can no longer use this HDD to replace PS4 internal hard drive. Seagate has removed internal SATA connection. I am somewhat confused why people were doing this. 7200 RPM laptop drives would be much better choice because of performance considerations. Like this one: https://www.amazon.com/Black-Performance-Mobile-Hard-Drive/dp/B01DOL05OC/ref=as_li_ss_tl?s=pc&ie=UTF8&qid=1487707269&sr=1-3&keywords=wd+hard+drive+laptop&linkCode=ll1&tag=codeproject-20&linkId=c409c09ff004693c145d4790073d011e

* This drive is compatible with Mac OS X, backwards compatible with USB 2.0, etc. In a nutshell this is standard 2.5 inch (laptop) NTFS-formatted, 5400 RPM HDD with USB instead of SATA interface.

I purchased this drive on August 25, 2016. It failed on March 1, 2017. After exploring all solutions with Seagate, they confirmed that the drive was dead. The only option they offered was a $500+ file recovery. Until I asked, Seagate did not even mention honoring the product's warranty.

Bought to upgrade my stock PS4 hard drive. Formatted, installed software, and transferred backup. Can confirm I backed up to an internal hard drive using an external drive dock. Works perfectly.

The 2TB Seagate Expansion Portable USB 3.0 hard drive is excellent expansion storage choice in an attractive package. This basic drive has a lot in common with other USB 3.0 compact drives including a similar price. This is the current model of the older and well received Seagate Expansion STBX2000401 still available on Amazon.

I have used a number of Seagate and Western Digital external USB 3.0 hard drives. Over time the newer drives tends to operate a bit faster than my older ones. That is my sense with this Seagate 2TB USB 3.0 drive when used with USB 3.0.

This drive has been used in a Windows environment and it plays very nice. Some older Seagate drives did NOT play nice on Linux systems unless the drive's sleep mode was disabled with the Seagate tools. If you plan to use the drive on Linux you may need to change the settings using Seagate tools on a Windows computer before use on Linux or sleep mode might cause loss of access until it is re-plugged.

In my casual testing (copying a 9GB folder of updates, iso files, and many mixed large and small files) performance is on a par with other recent Seagate and WD drives I have for my own business and for clients. At this point I think the USB 3.0 external drive market is pretty much a commodity space.

The drive fits easily in a pocket and as typical it uses a single cable for power and data making connections simple. The drive is compatible with USB 2.0, albeit at slower USB 2.0 speeds. The form factor for the drive is similar to the WD MyPassport Ultra and thicker than the WD My Passport Slim which are both more expensive. We are not talking about any big difference in size.

The drive comes packaged with the drive itself, a shortish USB 3.0 cable, a quick start guide, and 1 year warranty. No fancy premium software is included. Just the basics.

The Seagate Expansion 2TB is an economical commodity storage expansion. It clearly hits the target for the commodity USB storage market. Because it works quite well for a good price I'm giving this drive 5 stars.

UPDATE Jul 22, 2017:
In the about 2 and a half years since getting this drive it has continued to work fine in it's roles first as backup drive and next as a drive I carry in my kit when visiting clients. It's worked as expected whenever I've needed it and I've had no problems.

Since this drive was released as a top performer at the price in March 2015 this model has performed well but there are newer drives I would pick today. I see very few 2017 model drives from Seagate (or their subsidary LaCie). I've had very good luck with recent WD My Passport drives though they seem to have uglyfied their cases..

I think that while dated the Seagate Expansion drive has served me well and still deserves 5 stars..

Hope this helps someone.