I updated Eclipse with the new SDK tools (rev. 23), but now when Eclipse starts I receive the error:
This Android SDK requires Android Developer Toolk
I was getting the same "conflicting dependency" error on Mac OS X 10.9.3 and simply upgrading was not an option. What finally worked was downloading the latest Eclipse ADT bundle zip file from developer.android.com, extracting it and moving only "eclipse" folder to the place where my old eclipse folder was. (extracting the Eclipse ADT bundle zip file will give you "eclipse" and "sdk" folders).
If you decide to go the same route, first make sure you know what your Workspace path is. This can be found in Preferences. Then rename your old "eclipse" directory (not Eclipse.app) to something like eclipse-22.6.3, then move extracted "eclipse" folder into its place. Run new Eclipse.app inside, and when it asks you about Workspace, just enter the same path as you noted above. Or it can also be set later in Preferences.
Maybe worth adding is that to re-enable Android SDK Manager and Android Virtual Device Manager choose Window -> Customize Perspective -> Command Groups Availability and select Android SDK and AVD Manager. This will add these 2 items to the "Window" menu item for the current perspective (Java).
I didn't move the extracted "sdk" folder, because I already had sdk folder in the same directory as eclipse, which I have already updated to the latest Android tools. But if it makes you feel safer, you can also rename your old sdk folder (for backup purposes) and move the freshly extracted one into its place.