Registering / residence in Munich?

Good afternoon Munich!

I'm on my final steps of the move... found a house in Schwabing (yay!) and next week will get there.

My movers tells me that for customs purposes i need to register with the local municipality - can anyone tell me where to go, and what it entails? Having done the same in other countries it's generally a matter of showing up with an ID and a lease contract, is that the same?

Many thanks,
gianluca