Before you ever bought the property, you should have found out what kind of rental agreements or leases were being used there, but if you did not, during a visit you will want to establish how your relationship with the new tenants is governed. You should ask to see a copy of the tenant rental agreement if any. You may be awestruck when they produce one whereas the previous owner could not, so do ask. Look over carefully, understanding full well that you as the new owner are bound by it.

When you have inherited tenants, your business relationship with them is governed by one of four possibilities, the same as it might have been if the tenants had been yours from the start of their tenancy.

    1) Current lease
    2) Expired lease which has become a month to month agreement
    3) Written month to month agreement
    4) Verbal agreement
                             
No matter what kind of contract governs your relationship, you are governed by it for at least thirty days, that is, unless the previous landlord and the tenant had specifically agreed upon a shorter or longer period. If there is a lease involved, you are bound by its terms, whatever they happen to be, and for whatever period it covers, 1 week, 1 month, 6 months, 1 year or even more, like it or not.  In any case, you may not shove a new agreement at them and tell them they have to sign it right away and abide by it from that day forward. You have to give them time, that is their due.