Purchasing a property with MTM rental agreements

[Jon Coleman]

I just got my first accepted offer on a rental property and am working to get as prepared as possible before closing in a few weeks.  

When purchasing a property with month-to-month rental agreements, how do you typically handle those?  Do you have the tenants sign a new lease or do you keep them on the previous agreement?  Three of the four tenants have been living at the property for nearly a decade so I'm not overly concerned about them moving anytime soon but I'd also prefer to get all of them on my own lease so my bases are covered.