Inherited Tenants - How to give notice to vacate so I can live in the property

[Michael Swantek]

Hello! I purchased my first duplex and have a question regarding existing tenants. 

The summary is, I have an owner occupant mortgage. One unit has tenants I would like to keep (it is much larger and draws much better rents). The other unit is occupied by a tenant that has been there for years and is paying 150% or more less than market rates for rent. As far as I can tell this tenant has a handshake agreement at this point with the landlord prior to me. 

Given that I need to live in the home legally, I am planning to move into the smaller unit that is currently brining in the under-market rents. Any suggestions as to a process for "terminating" the lease or giving notice to vacate? 

Any suggestions, adhering to Michigan law is greatly appreciated.