It will work. Any EF lens will work on any canon DSLR. EF-S lenses work on crop body DSLR's only.
The focal length will be awkward on the Rebel though. It will go from not very wide to not very long. The 18-55 is a better match for most people (and about the same price, buy used and save a bunch, there are a million people looking to dump their 18-55's as they have upgraded).
EF 28-90 f/4-5.6 III is the kit lens that came with an entry level film-based EOS SLR. With crummy optical and build quality, not to mention wobbly focus motor, I don't see why you would want to bother with this lens.
I would stay away from this lens. If you haven't noticed, the 18-55mm that comes stock on entry line digital Rebels is the equivalent to the 28-90mm. The only difference is that one is made for digital crop cameras, and one is for full-frame/film cameras. An 18-55mm yields the range of 28.8-88mm, similar to the 28-90mm that you're looking at.
This 28-90mm won't be wide, or even long at the focal length, making this an odd lens for a crop camera. 44.8-144mm is the effective focal length on a 1.6 crop factor camera. You might as well pick up the 18-55mm, since you can find them for around the same price, or cheaper.