I dont know about the situation at your work, but if they have to find someone to replace you, it probably won't matter too much whether you've signed the new contract or not. Plus you'll presumably be there for at least half of your contract anyway, its not like you're leaving in a month!
You could always hold off an extra week on the announcement if it feels strange to you? I'm pretty paranoid about doing "the right thing" and I think you're fine!