In ASL we use the sign FINISH to represent completion. So in this case, we would state: ME FINISH EAT ME (using simple statement) or EAT FINISH. We typically place FINISH before or after the verb - so either way is okay.
You might nod more clearly if you're affirming that you have already eaten. If you're simply informing someone you have eaten (without being asked), you might nod much more subtly.