Got this one too, going from ADT 22.3 to 23.
Not sure what's keeping Eclipse from finding the updates (maybe some IDs changed or something), but the solution is to install the ADT plugins over the existing ones using Help -> Install New Software, just select the same site, no need to correct the URL from https to http or vice versa. The wizard will tell you there are a bunch of conflicts that'll result in removing the old versions of the plugins -- that's ok, go for it.
UPD Seemingly, (as at least one person downvoted the answer), installing new version over old one forcefully doesn't work for everyone. Here's the related bug where it's said that the old installation of Exclipse/ADT is hopelessly unupdatable and one should just download the new bundle to resolve this.
PS Anyway, you should be using Android Studio by now. Compared to Eclipse, it's a memory hog and has a very different feel to it and different hotkeys, but (as much as I hate to say it having been a snuggled up Eclipse user for a long time) it's way better, at least for Android development.