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. 
