Does Tenant Sign Rental Agreement The Same Day They Give Deposit?

[Lulu Heather]

Hello, I'm a new landlord and I'm wondering whether other landlords will make the tenant (who passed background, credit check) sign a rental agreement and all paperwork on the day they give you the security deposit? I have a potential tenant who will move-in next month, he still have 3 more weeks to move-in, but his application's been approved now. He needs to make all the deposits within 72hours, so at the day he makes his deposits to me, should I ask him to sign the rental agreement? Or he only needs to sign a Agreement to Execute Agreement? If so, when should I ask him to sign the rental agreements, at the exact day he move-in ?

I would love to hear you ideas, please. Thank you.