Google "post dating" or "postdating"
I don't know if postdating a lease has "legal effect" because I don't know what you are using it for. Who needs to see the paperwork?
Here is what I suggest:
When a tenant lives in a rental without a lease, he was a tenant-at-will. If you don't have a formal lease with your tenant (although he had a lease with the previous owner), in the past months he was a tenant at will.
Ask him to sign a letter, which state:
1. he lived in the rental property (address), as tenant at will
2. he paid rent of xxx every month to you (name, address), and
3. he moved out on 8/31/2014, and you are returning his security deposit of $xxxx.
Sign here and date here.