A bit late I know, but I've just been having a similar problem with a Samsung Galaxy S3 Mini.
This is how I got rid of it. I tried other ways, but found that if I turned the phone on and off again, the speech would come alive again. This was the only way I could kill it off for good.
Go to Settings -> Accessibility -> Text to Speech and there will be a list of current text to speech providers (I had 2, Google and Samsung)
Go to Application Manager -> All Find Google Text to Speech and disable it If there is no disable button, you will have to click Uninstall All Updates first, then go back, and the button should now read Disable You'll want to do the above step for each Text to Speech option you had in your list. I had 2, so I did it again for Samsung TTS.
Now if you go back to Settings -> Accessibility -> Text to Speech there should be nothing left in the list and your home screen will finally be silent. Hooray!
I also have driving mode and TalkBack disabled. I already had them turned off, but they didn't help.
Hope this helps.