Your agent should be able to assist with this, but typically you need estoppel agreements to transfer the lease from the existing owner to yourself.  If you have a property manager you are working with, they might be able to assist as well!  Hope this helps

Thats not accurate. An estoppel is just a verification of rent and security deposits. It doesn't have anything to do with transfer of lease. State law normally requires to lease to automatically transfer with the property. There typically isn't a need to sign new leases or do any formal transfers.

Not sure about your jurisdiction, but in Chicago most leases have assignment clauses. Reach out to your attorney to review the leases to see if anything needs done. 

If and when you buy the building, if there's any leases that have run month-to-month I would have the tenants fill out applications, requalify them and execute new leases with them. Remember to mitigate your risk at every step that you can.  

Like Adam said, some attorneys like to have estoppels signed to make sure there's no open tenant claims against the landlord, the deposits are accounted for and their rent is accurate and current. I like the idea of estoppels, but they're a PITA to get signed by tenants especially in class C and D assets. If the landlord has good records and they're having issues obtaining estoppels, it's not the end of the world. 

Good luck