Inherited Tenants - Lease Addendum?

[Bryce Moore]

I will be closing on my first duplex later this afternoon (finally). I hadn't really thought about this before now, but since one side of the duplex is already occupied - with inherited tenants - will I need to get them to sign an addendum to their current lease stating that I'm am their new landlord and that they will need to be making future rent payments to me? 

Up to this point I've had no real contact with the current tenants, but they do know that the property has been purchased by someone.