Asking renter to move out early so I can move in

[Suzanne B.]

We have unexpectedly decided to sell our personal home and will need somewhere else to live in the next month or two.  We own a rental property that has tenants who always pay late, we have to hunt them down to get rent, and they have done repeat damage to the home.  We were already planning to not re-lease to them when their lease ends.  My preference would be to ask these folks to vacate the property early so we could move in and have somewhere free to live until we find a new home to buy.  

Knowing them, I am positive if we offered cash for keys, they would move out early.  My question is: how much?  1 month's rent in cash?  2 months?  They will only have about 3 months left on their lease by the time they'd need to move.  

Also, will we need to draw everything up in writing and have them sign agreeing to the new terms, to over-ride our current lease agreement?