Inheriting a tenant that's not paying market rent...

[Jacob Henderson]

I am excited to say that I will close on my first property soon and will be inheriting tenants. The tenants and their two pets have been living there for 18 years and pay $475/month, no deposit, no pet fee and on an oral lease. I have spoken with an attorney who supplied an estoppel letter to me that both tenants were willing to sign. 

The market rent for this particular property is $700/month. My question is how do I approach this situation so that I can keep long term tenants but get closer to market rent for this property. I plan to ask them apply just like new tenants, have a deposit, but am willing to waive the pet fee since they have already had their pets living there long term. I want to have a paper lease signed as well. I have been debating back and forth on if I should do a month-to-month lease or annual lease and if I should gradually raise rent or just raise it to market value in one month. Like I said, I am new to real estate investing and would really appreciate any and all feedback on this. 

-Jake