What looks to have happened is the wood swelled (from rot/water) which created enough hoop stress on the concrete to blow out the corner. Since that part is not normally loaded, I wouldn't bother with the rebar suggestion. (If you already have a hammer drill, go ahead and do it; it adds <30 minutes to the job. I wouldn't buy one just for this job, though.) I'd pad the post with some compressible material that won't hold water [think a closed cell foam product] to allow for some further deterioration of the post without loading the concrete patch.
Then, provide some bond with the existing concrete (the suggestion for TapCons into the existing concrete would work well enough here; for load bearing applications, I'd use rebar, but here, screws are probably good enough), build a form underneath [at least] and on the sides [probably], and go to town. Use the edge trowel when the concrete is half-set. Don't expect the repair to be invisible. The patch concrete is finer and probably whiter than the existing concrete you have.
I've then used the following with good effect (and mine was on the loaded front edge of stairs that we use everyday in and out of the house, in a climate where we get freezing. The first repair (without TapCons) failed after about 2 winters. The second repair, where I used TapCons and paid more attention to not letting water get into the joint [with careful grading], has lasted 6 years and counting.
Patch product:
http://www.homedepot.com/p/Quikrete-10-lb-Vinyl-Concrete-Patcher-113311/100318504Flat trowel:
(Pick one. I'm not an expert and used the brick [diamond shaped] trowel I already had.)
Edge trowel:
http://www.homedepot.com/p/Marshalltown-6-in-x-3-in-Steel-Hand-Edger-HESG63-HD/202091765If you have the piece that broke off, you could try to pin it together with rebar and concrete patch, but you'd need to drill pretty good sized holes with decent alignment to each other and you might not have the [practically] needed hammer drill. I would consider that, but if doing that, would chisel away some of the base of the wood post and still provide the closed cell foam padding to allow a bit of play in the future to prevent it being forced off again in the next freeze or when the wood further rots/swells.
