Closing on tenant occupied duplexd

[Brenda Henry]

I am set to close next week on my first duplex property in San Diego!  The unit I will occupy will be vacant at close.  The other unit has tenants that have been in place for 3 years, paying market rents and on a month-to-month lease.  I have done my due diligence on the tenants, would like them to stay, and the previous owners have a thorough lease in place that I don't feel I need to make adjustments to.  

What is the best way to proceed?  Give tenants an introductory letter with contact information and a new month-to-month lease with the same terms?  California locals, can you advise...I understand there must be a 60 day notice to END a month-to-month tenancy, is there a same 60 day notice required to have them sign a new lease, or is it 30 days notice?

Brenda