Before doing anything major, try tilting the monitor up or down a little bit to reduce the visible backlight bleeding (this changes your viewing angle slightly which gets rid of some of the problem). I know it's not a perfect fix, but it can sometimes reduce it.
Anyways...
You might be able to find a different brand/model that does not have it so bad or even at all. I have seen some IPS that demonstrate this problem very badly and some not at all. Also, within the same brand & model, it possible to get panels with varying levels of backlight glow at 1-2degrees off-angle (depending on whether they happen to give you an A, B, or C grade panels I guess).
Still cookybiscuit is half correct. It seems to be a common problem with the new, cheaper IPS panels (e-IPS, H-IPS, and PLS), but it is definitely not something that panels must have and it is possible to make panels without this problem. The older S-IPS technology did not do this as far as I know. Unfortunately, I can't quite track down exactly which IPS technologies do this. I think it started with the e-IPS a few years ago; e-IPS was created as a form of "cheap" IPS panel and is a different design than the older (better?) S-IPS that was used for years... and then I think it continued with the H-IPS panels and then with the Samsung PLS (which copies the e-IPS or H-IPS). However, since that time, I have seen monitors using cheap IPS that didn't have the problem, which makes tracking it down even more complex.
What causes it: If I understand correctly the cause of this issue is the viewing angle on the new e-IPS, H-IPS?, and PLS panels (the ones with the rectangular pixels). For dark colors (like black) just a few degrees off-angle and the brightness will shift, causing the black to bleed through light in the corners (where the angle is 1-5 degrees) but not in the middle (where the angle is 0 degrees). Apart from this issue that people have termed "backlight glow" e-IPS, H-IPS, and PLS still have good viewing angles the rest of the time just like the older S-IPS did.
[Note: I *think* H-IPS is the same core technology as e-IPS, but could be wrong.]
Also, I have personally observed that some cheap IPS models do not exhibit any signs of this type of backlight glow (viewing angle shift), while others do ... so you may really want to try looking at another model in the store to see if you might find one. Also, I think the old S-IPS (which had chevron shaped pixels) did not have this problem. I can also confirm that the IPS TV I own does not exhibit this issue (I think it's the older chevron shaped S-IPS, but I may be wrong).
BTW, there is a second, unrelated problem with all IPS/PLS panels -- black levels. In general all IPS and PLS bleed through some light (not in corners, but evenly across the surface) and don't get as deep blacks as say an MVA panel. Technically, it is possible to get rid of this particular issue and get deep blacks by adding an A-TW Polarizer to an IPS panel, but very few monitors have this feature despite it having a huge impact on image quality. (BTW, they supposedly put this A-TW Polarizer in some tablets like the Kindle Fire HDX).
How big of an impact does an A-TW Polarizer have? It makes a big different as shown here:
http://forums.macrumors.com/showthread.php?t=1417898
BTW, if you are curious, there are pictures of various LCD types several posts down in this thread: http://www.avforums.com/threads/lcd-matrices-differences-and-what-models-are-placed.1113353/
Also, I wish we could somehow find out for sure which IPS panel technologies don't have this "backlight bleed" or 1-5degree viewing angle problem. I know I have seen them; I even own an IPS TV without the problem, but trying to figure out just which technology is causing this problem is getting a little too complex consider how little information the monitor manufacturers provide us with.