I don't know if it's identical to the posterize effect, but in GIMP, you can reduce an image to indexed color using a fixed, user-specified palette and then back to RGB.
Image->Mode->Indexed...
Select your palette. Set dithering to None. Hit OK.
Image->Mode->RGB
You might try adding a subsequent despeckle...I think that Posterize might do something along those lines as well.
EDIT: Okay, after running a test image in GIMP, and then examining histograms on the output is that it looks like what Posterize does in GIMP is to take a "number of levels" input, then strictly divide each channel evenly along those lines (e.g. for "3", you'll have 0%, 50% brightness, and 100% brightness for each of red, green, and blue channels), and then it reduces the number of colors using only those colors. I don't think that it does a despeckle. I used to enjoy making "more-poster-like" images than Posterize did, and usually did a despeckle to simplify them before running outlines on it, stuff like this:
But looking at a test image from GIMP posterization, it clearly has single-color single pixel regions, so Posterize isn't doing any sort of despeckling:
